Those are two diametrically apposed examples.
I admit there are some differences, to my knowledge no one has been forced to wear the yarmulke. And when asked to wear one at a wedding the only consequence of refusing might have been not being allowed in, or maybe not, I took it and wore it. They even let me keep it! However I think there are Muslim women who prefer to wear the traditional dress, for reasons similar to those who want to wear the yarmulke.
Muslims migrate to the US for a variety of reasons, escaping religious persecution is just one of many. One French Muslim woman ever sought asylum here so she could be allowed to wear her traditional dress. The article Muslim Immigrants (
https://cis.org/Report/Muslim-Immigrants-United-States ) in the United States does a good job of discussing all this, beginning with the first, possibly as early as 1501. Here are the reasons identified for more recent migration (cut and pasted from the article):
(1) Refuge. Tragic events in predominantly Muslim countries often lead directly to the emergence of a Muslim ethnic community in the United States; Afghanistan and Iraq offer particularly stark examples. The fact that Muslim countries are disproportionately dominated by dictators means that tyranny, persecution, poverty, violent regime changes, civil strife, and wars have driven some of the most talented and wealthy from Muslim countries in the Middle East, South Asia, and beyond.
Some examples by category:
- Ethnic persecution. Expulsion of Asians from Uganda, followed by smaller numbers from Tanzania and Kenya, led to some 6,000 Muslims arriving in North America. Saddam Husayn's extermination campaign against the Kurds led to mass exoduses in 1989, 1991, and 1996.
- Religious persecution. Hindu-Muslim clashes in India cause a steady stream of Muslims to seek safety in America, even as members of the country's elite leave due to job discrimination. There was even one case of a French Muslim seeking asylum in the United States.
- Islamism. Members of the Ahmadi sect fled Pakistan when their faith was deemed not Islamic in 1974, as did many other Muslims running from the Islamist (or Islamic fundamentalist) dictatorship of General Zia ul-Haq. The Iranian revolution of 1979 targeted the sort of person most likely to seek refuge in the United States. Persecuted by Islamists, members of anti-Islamist movements such as the Republican Brothers of the Sudan and the Association of Islamic Charitable Projects of Lebanon, immigrated to the United States.
- Anti-Islamism. Conversely, Islamists flee repression from countries such as Algeria, Egypt, Lebanon, and India by moving to the land of the infidel, where they (ironically) find the freedom to express their views.
- Civil wars. Waves of immigrants arrived as a consequence of the endless civil war in Sudan, the 1971 Pakistani civil war, the 1975-90 Lebanese civil war, the 1990s anarchy in Somalia and the former Yugoslavia.
- International wars. The Israeli victories in 1948-49 and 1967 caused waves of emigration. The Soviet invasion of Afghanistan in December 1979 and the decade of warfare that followed prompted the educated to flee. The Iraqi invasion of Kuwait in 1990 brought not only Kuwaiti citizens and residents, but also 10,000 Iraqis, one-third of them soldiers (and their family members) who surrendered to the Allied troops and could not be sent back without imperiling their lives. With the Muslim world dominated by dictators, it seems unlikely that this flow will end or even lessen any time soon.
(2) Education. By the 1990s, U.S. colleges and universities attracted over half a million foreign students, many of whom chose to remain in the United States, where facilities for their profession are superior, political freedoms wider, and economic rewards greater. Among medical students, more than 75 percent — and perhaps as many as 90 percent — end up staying in the United States. Female students are also particularly inclined to stay; they appreciate the independence, self-sufficiency, and opportunities for assertiveness the United States offers them and know that to return means having to conform to restrictive ways, demure behavior, and family dictates.
(3) Islamist Ambitions. Although the numbers in this category are smaller than refugees or students (and indeed, some Islamists also fit in those two capacities), Islamists have particular importance, for they harbor religious and political ambitions that are in a potential collision course with the majority population.