The US was in the minority in doing this. Just a quick look reveals the following major airlines not diverting at the time:
TG, SQ, MH, KL, VN, TK, QR, AI, DY, BR, EK, LH
And thats not even all of them
Hell UA was flying over Baghdad to KWI during times that were quite a bit more volatile and Anti-US than this
Backed by Russia doesn't matter as a reason to not fly over because Russia didn't give them weapons capable of downing a civilian airliner at that altitude
Diverting around every possible area of conflict where someone might get their hands on something that could shoot down an airliner is not really a possibility. Plus the odds are incredibly small that something like this will happen. There are over 100,000 flights a day world wide. How often does this happen? It was more dangerous for you to drive to work today than for MH to fly over the Ukraine.
FWIW - this is a fairly frequent flight. I think once a day