In the decade before the population transfers between Greece and Turkey that began in 1923, those two countries had fought each other in the First Balkan War, the First World War, and from 1919-1923 in the Greco-Turkish war.
Since the Greek state was so often at war with Turkey in this period, were Greek Muslims viewed as unpatriotic or possibly loyal to turkey by the Greek government or Christian neighbors?
Were there any regulations passed to control the movement of Muslims, and were they passed as "war necessity"?
I haven't looked deeply at this issue myself, but I can give you a couple of places to look. I mostly look at this issue from the other side: minorities within the Ottoman Empire, rather than Muslim minorities trapped outside of its borders. In that specific time frame, I really know little about Greece's political history, never mind the details of social and cultural history. I can say that in the late 19th and early 20th century, we see increasing nationalism, increasing support for the Megali Idea, so I can only assume this had effects on minorities like growth of nationalism often does, though I don't know details of legal measures taken before the population exchange.
I can tell you the first two places I'd look. First, would be Justin McCarthy's book on the Ottoman Muslims who ended up outside the Ottoman Empire: Death and Exile: The Ethnic Cleansing of Ottoman Muslims, 1821-1922. McCarthy is a controversial figure in some circles, as he is perhaps the last Western historian who doesn't characterize the ethnic cleansing of Ottoman Christians from Western Anatolia as "genocide" (for all the controversy of his "denial", he readily estimates that 600,000 Armenians died due to Ottoman expulsion, for what it's worth). However, he's probably the authority on the ethnic cleansings of Muslims in the Balkans and Caucasus, including Greece. Unfortunately, he mainly does demography, and I'm not sure how detailed he'd go into the social and legal change. I have only looked up a few numbers in that book and don't have it handy.
The second place I'd check is Bruce Clark's Twice A Stranger: How Mass Expulsion Forged Modern Greece and Turkey is often considered the best English book on the population exchange, but I've never read it (it's also, fair warning, pop-history by a journalist, rather than an academic). Because so much of that decade of war was fought on Ottoman/Turkish soil, there was always a great focus on the Ottoman minorities, rather than the Greek minorities who were more distant from the front lines. I'm not sure what this book says about them. There's the edited volume Crossing the Aegean: An Appraisal of the 1923 Compulsory Population Exchange between Greece and Turkey, which I have looked at, but I only remember it covering events after the exchange, not the ones that lead up to it (the table of contents seems to confirm this memory).
I was going to recommend a primary source for you as well, because in the late 1920's, the League of Nations authored a series of reports on the various refugee problems of the region: Greek Refugee Settlement (1926), Armenian and Russian Refugees (1926), Armenian Refugee Settlement Commission Report to Council (1926), Conference on Russian Armenian Refugees (1926), Scheme for the Settlement of Bulgarian Refugees (1926), Report by Dr. Fridjof Nansen (1925), and several others, but of those, only one volume seemed to deal with Turks or Muslims, Report of the Advisory Commission to the High Commissioner for Russian, Armenian, Assyrian, Assyro-Chaldean and Turkish Refugees (1929). I haven't look at it, but from its title I would guess that it covers Turkish refugees briefly, and does little to cover how they got that way. When looking at the case of expelled Greeks from Turkey, I had mostly just used these reports to double check other people's citations of the quantitative side of the crisis.
This is why I love this sub--this is a very interesting and obvious question that I had literally never even spent a single moment considering. But I'm afraid we both need a Greek historian for a better answer! From this, it's clear that there were Greek elections in 1915 and 1920 where Muslim deputies were elected, especially in the "New Lands" acquired after 1913 (so they had no been deprived of their political rights, whatever social censure they faced). According to that same source, it seems that the Muslims supported pro-monarchy parties (except in Crete, where they voted for the nationalist Venizelos). But even though they generally didn't support the Venizelists, the Venizelists still campaigned for their votes (as well as Jewish votes in Salonica, where the Jews made up an important and substantial population before their almost complete destruction in the Holocaust). In 1920, the Muslims apparently switched their support for the Socialists. This book says that only after the Greek started to lose the War in Asia Minor did the government and popular sentiment turn against Muslims in Greece--this led to, among other things, the Muslim mayor of Salonica/Thessaloniki being taken from office and put in jail, alongside the Mufti. Many other Muftis were also removed and replaced, some others even put in jail. The Revolution of 1922, created separate ethnic electorates for the Muslims of Thrace and the Jews of Thessaloniki.
If this is accurate, this wide spread, officially sanctioned discrimination is rather late and, considering the exchange, brief for most once-Greek Muslims. I wonder if there was a difference in treatment between the countryside and the cities, however. In the Ottoman Empire, the Christian minorities in major urban areas (Istanbul, Izmir, and other central cities) did not face the same persecution that Christian minorities in the peripheral cities and rural areas suffered.