This is the video in question. Among other things, such as someone in the audience yelling "Let him wear it!" in reference to the head of the Muslim Brotherhood, the general attitude of both Nasser and his audience seemed to be that making the Hijab mandatory was a dumb idea. Nowadays, Hijabs are worn commonly by Muslim women all over the world. What caused this shift in attitude?
This shouldn't discourage answers because I'm really curious about Egypt and other places with "state feminism" like Tunisia and Algeria, but here are some of older posts on a similar subject:
Did majority of women in medieval Islam not wear hijab? I ask this because majority of women in 20th century Muslim countries do not wear hijab until recently (look at /u/sunagainstgold's post here as well).
Mustafa Kemal Atatürk was the first leader of an Islamic country (Turkey) to impose restrictions on Islamic garb. Atatürk banned the fez (for men), and had the army forcefully shave the beards of mullahs in the streets of Istanbul. For women, Ataturk imposed restrictions on the chador and hijab.
Atatürk of course didn't appear out of a cultural vacuum. Before him, the Ottoman empire had made attempts at modernization. These were never successful, and the Ottomans retained the epithet of being "the Sick Man of Europe". Ottoman provinces were gradually carved off by European imperial powers, until finally - in the aftermath of WW1, Turkey itself was to become a ward of the victorious allies. Ataturk stepped in, and his improbable yet successful defiance of the reigning order earned him immense gratitude (Atatürk literally means "Father of the Turks", and it was an accolade bestowed upon him after Kemal's rescue of the country from colonial powers).
Turkey had previously been the seat of the Ottoman Empire (which also laid claim to being the Islamic Caliphate), so the idea of unifying Islamic countries under Turkish rule (again) was never popular. But, Turkey's success under the Kemalist doctrine of secularization and a strong military became the blueprint for modernists in other Islamic countries - from Egypt, to Iraq, to Syria, and Libya. All of these countries transitioned to a republic model, led by a former soldier.
When Atatürk died in 1938, he lacked an apparent heir as a modernist leader of the Islamic world. Mossadegh in Iran appeared to show promise offering a conciliatory path toward modernization for an Islamic (Shia) state, but the colonialists had him replaced.
Nasser took power in 1956. That same year, he defied the colonial powers by nationalizing the Suez canal, and humiliated the UK and France. With this act, Nasser essentially seized Atatürk's mantle as the visionary who could lead the Arab and Islamic world back to a place of respectability. His esteem was so great that Syria basically threw itself at Nasser's feet, joining him in creating the abortive United Arab Republic.
Nasser died in 1970. Many Arab countries gained leaders under the Atatürk/Nasser mold - Saddam Hussein in Iraq, Qaddafi in Libya, and Hafez el Assad in Syria - all military men with a vision for secular republics. But, none of them ever successfully defied the imperial powers.
In 1979, the Ayatollah Khomeini took power in Iran, deposing the CIA-installed Shah. For the first time since the Ottomans, Islam provided a path for successfully defying the Western powers. The Islamists were far from being the only group to oppose the Shah, but they had one advantage - the Shah had let the mullahs maintain some organization, while secular groups (who were perceived as a more dangerous threat) were routinely infiltrated and decapitated.
The same year of the Iranian revolution, Zbigniew Brzezinski started to assist Islamists in Afghanistan, hoping to provoke a Soviet intervention. This ploy worked, and for the following decade, it was Islamists who defied the USSR.
In Libya, Egypt, Syria, and Iraq, ossified secular regimes have faced an onslaught from Islamist circles that claim a moral right to govern, and the regimes have been unable to reply.
Perhaps one of the most ironic elements of this dynamic is that much of the funding for the various Islamist insurgencies has been provided by the monarchies of the Gulf States, who have been anxious to prove their piety by funding extremism abroad, while preaching conservatism at home.
I can't say I know much about Nasser's personal position in relation to hijab (except that he wasn't particularly religious, and his daughters never wore any), but a little bit about Nasser and his relation to Moslem Brotherhood.
The essence of the problem between them was a power struggle.
As of the early 1950s, Nasser was in charge of the Free Officers Movement. This originally consisted of officers with very different ideological backgrounds. Most were Arab nationalists (and fiercely anti-British), many were republicans (i.e. against the monarchy), but there were also religious people (indeed, some were close to the Moslem Brotherhood), leftists etc. What they all had in common was that they saw themselves as 'modernizers'. They based this idea on understanding the military service as a model of a 'disciplined', 'professional', and 'efficient' force in Egypt: a force that reflected the military characteristics of cohesion and dedication - which were qualities considered 'rare' (if existing at all) in Egyptian public life not only by foreigners, but especially by the officers in question (see Nasser's The Philosophy of the Revolution). From that standpoint, King Farouq, all the royalists (or even those just loyal to the crown), and representatives of various other political parties and movements (Egypt was a parliamentary monarchy as of the late 1940s and early 1950s), were all 'corrupt', 'incompetent', 'useless', 'thieves' and 'traitors' (here I'm citing an e-mail from a contemporary officer of the Egyptian Air Force, who in turn cited one of Nasser's public speeches).
Now, when the Free Officers decided to stage a coup against King Farouq, in July 1952, they thought that they need a well-known, popular character as a new leader of the country in place of the king. Specifically, Nasser was convinced that a relatively low-ranking, unknown officer like himself would not be accepted by the Egyptian people. Indeed, that even the military was unlikely to follow somebody like him. Therefore, they picked General Mohammed Naguib as their 'official leader'. Naguib was one of few Egyptian heroes from the Palestine War of 1948-1949 and popular in wider public.
So, when the Free Officers Movement removed Farouq, in late July 1952, Naguib was declared the President, the Prime Minister, and Chairman of the 9-member Revolutionary Command Council (RCC), while Nasser was appointed Deputy Prime Minister and Minister of Interior.
Unsurprisingly, a major rift developed between them in a matter of weeks (if not days). Namely, the RCC's original idea was to remove the king and install a parliamentary democracy and Naguib insisted on this solution. However, other members of the RCC became concerned about influence of various political parties (especially the Wafd, but also the Moslem Brotherhood, Communists etc.). Nasser & Co won this first round, and dissolved and banned all the political parties, in January 1953, announcing they would rule during a transitional period of three years.
The Moslem Brotherhood reacted with a campaign of civil tumult (not only 'unrest'), and de-facto opened a battle for popular support. It could be said that they began winning this battle: as riots spread, the RCC came under such a pressure, that it decided to outlaw the Brotherhood, in January 1954.
However, it was around the same time that Naguib began secretly collaborating with the Brotherhood and preparing a coup against Nasser. Thus, the next round of political struggle between the two followed, known as the 'March Crisis'. It ended with Naguib retaining the position of president but losing whatever authority he once held.
In attempt to improve his standing in the population, Nasser then did two things:
a) he published the above-mentioned book The Philosophy of the Revolution, in order to make public his ideology of Arab nationalism, anti-Imperialism, and Egypt's central position in the Arab world, in Africa and in the Islamic world, and
b) he opened negotiations with Great Britain over the status of the Suez Canal Zone, where 80,000 British troops were still based (much to disgust of nearly every single Egyptian).
These negotiations were concluded in July 1954, with the British agreeing to withdraw from the Suez within two years ('in exchange', Egypt gave up all pretentions to suzerainty over Sudan and most of the Nile Valley). A corresponding treaty was signed three months later, and Nasser rushed to make this public.
That was the opportunity for which Naguib and Moslem Brotherhood were waiting for: they sent one of Brotherhood members to assassinate Nasser while he was delivering a public speech in Alexandria, in late October 1954. The gent in question missed with all eight shots. Instead of running away, Nasser maintained his pose and delivered a speech. That made him a hero in the population. Immediately afterwards, he ordered the biggest political crackdown in history of modern Egypt: he not only put Naguib under house arrest, or dismissed about 150 officers loyal to the pressident, but also ordered arrests of thousands of Brotherhood members, Communists, former members of the Wafd party and all other sorts of - true or perceived - oppositionals. Once this process was complete, he was elected the president of the RCC, and appointed the President of Egypt, in January 1955.
From this, it's on hand that Nasser was no big friend of the Brotherhood - nor (most) of its ideology. Question is: what caused that?
Well, from chatting with dozens of Egyptian officers (in the course of research for the book-series 'Arab MiGs'), it transpired that due to decades of supervision by the British, they became sort of 'Westernised'. This is something none of them would readily admit (they were too much Arab nationalists and anti-Imperialists to do so), but it was simply so that hardly anybody between Egyptian military officers was religious. Many were educated in the UK, and British influence could be seen in many of them enjoying their drinks in the evening - and not only in their uniforms or (in the case of the air force) ranks, insignia etc.
What changed this was the catastrophic defeat during the Arab-Israeli War of June 1967 (a.k.a. 'Six Day War'). Until that war, being an officer meant prestige and enjoying state-sponsored privileges. After that war, the military was in tatters and officers deeply ashamed. More importantly, most of them (at least those that didn't openly side with Field-Marshal Amer, who was subsequently sacked) lost their hope that Nasser and his 'laicist' approach to ruling the country would eventually result in some sort of better future for Egypt. Most of officers remained loyal, but they concentrated on exercising their profession instead, and many - gradually - found 'refugee' in religion.
To a certain degree, this process was bolstered by another decision related to that war: namely, the Saudi conclusion that Israel won that war by a religiously motivated military, and that therefore Arabs/Moslems should create a similar, religiously motivated military on their own. That's why Saudis subsequently began sponsoring establishment of religious schools all over the world, but foremost in the Middle East, of course...
The next impetus for 'reverse development in public attitude' was delivered by nobody else but Egyptian President Sadat. Namely, while this 'back to religion' trend was temporarily stopped by what Egyptians perceive as a 'victory' in the October 1973 War, during the 1970s President Sadat found himself facing widespread popular unrest. Because of this, he began cooperating with the Moslem Brotherhood in order to maintain himself (and the military) in power. Thus, and for example, it was something like 'over the night' that wearing hijab became 'popular' on the universities - while 'progressive' students (most of whom were involved in protests against Sadat) were de-facto forced to 'shut up and behave' by Brotherhood's activists. Certainly enough, Sadat's flirtation with Brotherhood ended rather bad for him (he was assassinated by Islamists in 1981), and Mubarak subsequently launched another crackdown against fundamentalists (including a little-known campaign of air strikes against certain of their strongholds, in Upper Egypt). But, by then it was kind of 'too late' - also because the Brotherhood began receiving direct support from Saudi Arabia. Indeed, this 'Saudi-Egyptian Fundamentalist Axis' eventually produced the al-Qaida.
Followup question, but did the leader of the MB actually ask him to do this given the antipathy between Nasser and the MB at various times eventually leading to him suppressing the group after one of them tried to kill him?