People aren't equal though. Coming from Russia, the West is really confused about what it wants.
It seems to want chivalry plus equality minus morality. This desire is represented by factions who seem to work together on some level. The end result is a mess.
A mess the end result of which is that people here touch far more rarely than they did in Victorian times. Yet we know that rarely being touched in childhood is a strong risk factor for promiscuity later on.
As for equality, women are far more at risk from sexual predation and assault; I don't think it's rude to let social customs reflect this by having them initiate touch, largely.
Democracy is messy, slow and complicated because it's build upon compromises between different factions. A lot of things in the west are more of a mess than they are in Russia, but there is a reason immigration streams one way.
Equality in modern colloquial context (esp. regarding social strata) means equal "especially in status, rights, and opportunities". It really means fair treatment, not equal treatment. Another side effect of people using the wrong language and sticking with it.
It seems to want chivalry plus equality minus morality. This desire is represented by factions who seem to work together on some level. The end result is a mess.