I think it's disingenuous to say there's no difference between celebrating your cultural origins and refusing to adopt American ideologies.
I'm of Finnish descent. I have a Sisu bumper sticker and eat pulla. Do I refrain from making small talk with strangers at a bus stop? Of course not! Americans tend to be more open to strangers than Finns.
The problem is that it's so easy for bigots to conflate one with the other - if you see some lady in a headscarf she might just be carrying on the sartorial tradition she grew up with, but a bigoted person might say she's a harbinger of Islamic radicalism.
And there's no question that such radical Islamists exist, are generally strongly against the western-liberal-pluralist tradition, and that some of them are willing to commit heinous acts of violence. It would be a logical mistake to conclude that every Islamic person must necessarily be an extremist, but sadly it's not hard to think of politicians and pundits willing to mine that particular fallacy for all the political capital they can extract from it, and sadly there's a large portion of the population that is too dumb to spot the difference and who can easily be talked into scapegoating anyone who looks or acts differently, regardless of whether they actually pose any danger.
I'm of Finnish descent. I have a Sisu bumper sticker and eat pulla. Do I refrain from making small talk with strangers at a bus stop? Of course not! Americans tend to be more open to strangers than Finns.