While I was living in Russia, I observed that Russians tend to have harsher views toward LGBT individuals. I'm not sure whether this is truly the result of Putin's anti-LGBT ideological propaganda or due to geographic or cultural factors. But it's interesting that Trump shows a similar attitude.
On individual level of views this is where this two leaders D. Trump and V. Putin shares similar resentments on the idea of LGBTQ and can gladly shakehands about it. In contrast to Russians apart from Putin stand against LGBT the Russia are people with strong priority to their culture and norms. Americans are too flexible in embracing different ways of life onto self-freedom opposed to strict morals. This explains why their views on LGBT regardless of Trump stands against it.