“If they’re refugees, they wouldn’t be able to vote.”
WTF? Being a refugee makes path to citizenship and voting even faster, not slower. often just a couple of years. A Refugee immigrant is much more likely to be a US citizen than other immigrants!
Also Perhaps not at the moment in federal elections, but in my area non citizens vote in local elections. Have you looked at the voting laws lately? There are many elections in which non citizens can vote.