Not really — we don’t use “because” and “makes,” because that’s redundant here. Here are some ideas:
Because of (or “thanks to”) my family background, I like making friends from other countries.
I’ve put “friends from (or “in”) other countries,” or you could say “friends from abroad,” or “international friendships” because most of the people on italki are in their own countries, so we are not “foreign." From our own point of view, we are no more foreign than you are.
By the way, in your introduction, you use the word “problem” (as a translation for 問題?). In fact, you probably mean “question.” “Problem” has bad connotations.