Huh... the few Americans of Russian descent I've met have actually all be quite socially liberal, and I've generally attributed it partially to the fact that communism left a relatively secular legacy in Russia. But it seems that as that legacy fades, Russia is going back to what it was before World War I... one of the most illiberal countries in Europe.
On some issues (such as abortion; though abortion never was a significant political issue) Russians are still fairly socially liberal. But on many (probably most) other issues Russians were socially conservative in Soviet times as well as currently. Religion isn't the only ground for homophobia, so secularism (Russian population is still low religious) isn't panacea for homophobia.