You actually just need the OTL U.S government- some Muslims did immigrate to America in this time period, just not in the numbers in this challenge. The article I linked to is about how some of them settled in North Dakota.
But if you have large-scale Muslim immigration, the government likely will respond with restrictions, as it did for Chinese and Japanese immigration in the 19th century. I don't think the OTL government was necessarily tolerant of Muslim immigration in the abstract; there just weren't enough Muslim immigrants for it to take notice.