Because you can define a whole nation by one tweet? The level of racism here is similar to that in Barnsley in the 1980's. Not good, but hardly rendering the place a no-go zone. Very surprised to hear something like that coming out of Moscow mind. In the provinces? Certainly. But Moscow and St Petersburg folk generally tend to be a bit more enlightened.
No but you can get a sense of the culture from numerous sources, not big on free speech and gays either.
The country is not without its problems, and the two areas you mention, along with racial tolerance, are definitely on the "could do better" list. However, there are plenty of liberal media outlets if you know where to look, and there are a couple of gay clubs in St Petersburg which are easily as camp as anywhere I've been to in Britain, and super friendly to boot. Do you really think I would have lived here voluntarily for 14 years if it was anything like the place it is portrayed to be in the media?