The wikipedia page on the arab slave trade speaks of millions of africans being bought, and as there doesn't seem to be rigid race divisions in the american fashion, then I'm guessing they have mostly intermingled with the population over the years.
Which leads to the title of this post, about how people looked like prior to this trade. On a side note, people often criticize depictions of jesus for looking too white, could this have anything to do with that?
This question is predicated on several assumptions, some of which are not necessarily accurate. It is true that the 'Arab' slave trade from the 7th to 20th century resulted in the enslavement of millions of sub-Saharan Africans, however the fate of these slaves varied widely and was dependent on the geographic location in which they were transported to and sold, the time period, the wishes of the buyer, and so on. In many cases, African slaves did indeed assimilate into whatever Muslim society they ended up in. Take the case of the Arabian Peninsula, where there are numerous examples of sub-Saharan Africans assimilating into Arab Muslim society. The mother of the Saudi prince and former ambassador to the United States Bandar bin Sultan was an Ethiopian concubine. The mothers of the Qasimi Imams of Yemen were similarly African concubines. According to the German cartographer Carsten Niebuhr who visited Yemen in 1762, the Imam al-Mahdi al-Abbas (d. 1775) 'was of dark complexion, like his ancestor's by his mother's side, and did not at all resemble the other descendants of Mahomet.'^1 The Sunni coastal population of modern Yemen has historically had strong economic and cultural connections with the Horn of Africa, the Swahili Coast, and India; and they are stereotypically darker-skinned than Zaydi Yemenis from the highlands.
That being said, the Middle East is a big place and the Romans never ruled the Arabian Peninsula (perhaps barring a few peripheral areas). African slaves did not always end up having children. Some were eunuchs and others were used as soldiers. In some cases, sub-Saharan Africans and their descendants formed small minority communities, e.g. the Siddi in India and Pakistan. It is probably impossible to measure how many Africans 'intermingled with the population,' though clearly such did take place and in certain regions more than others.
Furthermore, Africa was definitely not the only source of slaves in the Islamic Middle East. Other prominent sources of slaves included the Caucasus, the Turkic peoples of Eurasia, the Balkans, and other parts of Europe. During Ottoman times, the political and military ruling class was dominated by men of Balkan and Caucasian origin and many settled in places like Anatolia and Syria where they became the founders of important local dynasties. The 'Khedival dynasty' of modern Egypt was of Albanian origin and the mother of Reza Shah Pahlavi (d. 1944) was Georgian. The Mamluks and Safavids also imported slaves from the Caucasus. Also, in the 19th and 20th centuries millions of Muslims from the Balkans, Crimea, and the Caucasus left their homelands (sometimes forcibly, sometimes voluntarily) and settled in the Middle East. Arabs in the Levant of Bosnian origin sometimes have the last name Bushnaq.
So, in conclusion, I can't really give you a definitive answer on whether the 'phenotype' of the average Middle Easterner changed since Roman rule. More importantly, it is difficult (and often inaccurate) to make any generalities about the nature of slavery in the Middle East. Slaves were taken not just from sub-Saharan Africa but also from the Eurasian steppe, the Caucasus, and Europe. Also, I did not mention this, but it is anachronistic to take categories like 'white' and 'black' race and apply it to premodernity.
Since Bardizbeh has given a very good answer to this question, I'd just like to address the small point: "On a side note, people often criticize depictions of jesus for looking too white, could this have anything to do with that?"
People criticise the way that, in the West, he is often presented as a Westerner, with a western nose, light hair (sometimes blonde), etc. Because presumably, he did not look like that, being a Middle Eastern Jew. (Similarly, in Ethiopia, he is often depicted as an Ethiopian.)
The reason he is depicted as white has nothing to do with people originally thinking he was white*. We have no idea what he looked like, other than the guess that he looked typical for a Middle Eastern Jew of the early 1st century AD.
Here are some of the oldest images of Jesus: https://churchpop.com/2015/03/09/6-of-the-oldest-images-of-jesus/ (That's hardly a reliable history website, but those are some of the oldest images of Jesus in one place for you to see)
No detailed images of him appear until hundreds of years after his death, and by that time people simply depicted him as a bearded (to denote wisdom), handsome person who looked similar to whatever they looked like.
Thus, he looks rather Mediterranean, but not particularly Jewish, like the people making these images.
So, even if by some unlikely coincidence Jesus was in fact blonde-haired and blue-eyed, that would still have no relation to him being depicted as such.
*Not that people in the Roman Empire really thought of people as "white" at all.
Additionally, did people in North Africa have darker skin before the Romans came?