There's two major axes, here.
The government is pushing the 'Ukranian neo-nazis' propaganda, because it's a convenient bullshit excuse (as is all the spilled ink in Putin's essay about long-dead history). Some soft-headed people obviously believe that wholesale. What isn't an excuse, though, is that Ukraine did take steps to restrict its Russian minority. Many Russians who don't swallow the neo-nazi nonsense are sympathetic to that view on the situation (for, uh, obvious nationalistic reasons).
Now, whether or not sympathy for that is sufficient grounds to do nothing and respect Ukrainian sovereignty, to prosecute a proxy war, a limited war, or a full war all depends on how much of a warhawk you personally are.
My highly unscientific feeling is that public support rests somewhere north of 'most Russians believe that Ukraine has been repressing Russians, and would support a proxy war', and somewhere short of 'drive the fascist swine out - prosecute a full war and occupation of Kiev'.