The attitudes are similar. People in Russia aren't going to jail for being gay. Every now and then they've jailed people for staging gay pride parades without a permit, but those sentences are just like here - they're not long-term.
Also, although the majority are generally tolerant in both places, hate crimes happen in both places from time to time.
I lived for 11 years in the South and visit regularly. I also visit Russia regularly and most of my friends are from the former Soviet Union somewhere. I know what I'm talking about.
You also are misstating the situation in Russia. There is not a return to communism in general. Most enterprise is in private hands. The problem is that the state has too much ability to interfere in that private business. In this respect Russia has never changed. The tsars maintained government monopolies in certain areas and tried to direct everything top down. The communists took it to an extreme that no one wanted to see, but Putin is still following in Russian traditions regarding the power of government. I don't know, it could have something to do with the geography of Russia - a very cold climate, a lot of land, poorly defined natural borders - that creates this centralization of power. It could also have something to do with the way Russians erode any power they see as weak at the first opportunity they get. Either way, my issues with Putin are that he just uses these convenient precedents rather than trying to move away from them.
ἡ δὲ κἀκ τριῶν τρυπημάτων ἐργαζομένη ἐνεκάλει τῇ φύσει, δυσφορουμένη, ὅτι δὴ μὴ καὶ τοὺς τιτθοὺς αὐτῇ εὐρύτερον ἢ νῦν εἰσι τρυπώη, ὅπως καὶ ἄλλην ἐνταῦθα μίξιν ἐπιτεχνᾶσθαι δυνατὴ εἴη. – Procopius
Ummaka qinnassa nīk!
*MySmiley*