Have they lost a lot of influence? Can for example a non-christian become president of the US?
Doesn't have to be a muslim, hindu or what not. Simply an atheist a person with no background or interest in religion. Southern american countries, abortion laws there are still not great, not just southern american though, look at other nations like Spain or Italy where you see a heavy influence from the church regarding some matters, being it again women rights or gay rights. Or take a look to the east, Poland same story there.
Sure the pope may no longer directly influence who rules a country but Christianity is sadly far from gone.