Even minor cultural differences can cause clashes. I think it's worth it to try to work through them. I can't dictate what others choose to do.
My daughter lost a friend a while back over personal differences, at least some of which were cultural. I did my part to try to help them get past it, but you can't force people to get along.
While her friend isn't an "immigrant", her family is a blend of a couple of cultures which are just different enough from my daughter's culture to create a bit of friction here and there. I suppose it was too much friction for a couple of intelligent, but bullheaded, girls to get past. I may have been more upset over the split than they were.
It made me think back to my own younger days. When I was a teen my family befriended a family who had recently moved from Iraq. We hung out a lot and learned quite a bit from each other (I still remember how to count to ten in whatever language they spoke, as well as several other words) and shared recipes and meals. My sisters and I had a great time with them with no problem.
But, there were some incidents between the adults that caused a rift between our families. At the time I wasn't aware of what had happened, I just knew we suddenly stopped hanging out with them. When I got older I found out what had happened. The fact that their parents didn't understand why my parents would be upset over it was what caused the final rift. That seems cultural to me.
I still enjoy being exposed to other cultures. I think all cultures have good points and bad points, plus some things that really aren't good or bad, but that I just don't personally care for. I mean, I despise professional sports and government employee worship, two things that seem rampant in the culture that surrounds me-- so it's not just "alien cultures" that I find fault in.