It does now for the very clear reasons:
1. NATO, while being openly hostile towards Russia (you may read the current NATO's doctrine where Russia is named as the #1 probable enemy of NATO), attempted to expand to Ukraine, which is just not acceptable (to Russia) at all.
2. Russian nationals (and Russian speaking Ukrainian nationals) got oppressed in Ukraine, but that happened mostly as a result of the division of country into two parts where one was pro-Russian and the other was pro-West (EU, NATO).
I don't think the 2nd reason would even occur, since if Russia was in NATO - it would rather even seek Ukraine then joining it too. There would be no 'maidans' (coups) in Ukraine, there would be no division of the country and thus the oppression of Russian nationals (and Russian speaking Ukrainian nationals) just wouldn't have taken place then.
I think the conflicts concerning Russia then would rather shift towards Middle East (like Turkey having some beef with Russia over who supports whom in Iran, Palestine, Israel and so on) and maybe towards China/India.