It is also not false that people only care about the problems around them and that could negatively influence on their lives.

That’s not really a “people” problem. What you are saying is a projection. Much of the Middle East, for example (and especially Syria), warmly welcomed refugees from Greece, Armenia, Circassian, etc just as well as they have received refugees from Arab countries like Iraq, Kuwait, etc.

So yeah, not everyone is racist and checks someone’s ethnicity or skin color before helping.