You're right, the US has a low rate of immigration and should be able to handle it, but that's not necessarily the case.
Also, 0.3% per year amounts to nearly 8% over one generation, not including differences in fertility between immigrant groups and born Americans.
And you're right about the 8%, but since only about 10% of immigrants to the US are Muslim, really we're talking about 0.8%, over something like 25 to 30 years. That is so completely disproportionate to the hysteria over immigration (literally the number one issue for Trump voters, IIRC) I can't help but conclude that it's a purposeful scare campaign.
Also, it's not often that any immigrant group is the boogeyman for more than a generation. It used to be the Irish, then the Polish, then the Puerto Ricans, and so on. A huge fuss is raised, and then they assimilate, at least in the US.
In no way is that a "large, rapid" influx. This whole issue is just political football and scare-mongering.