In the US, issues like abortion, gay marriage, and other issues are (usually) divided on the typical Republican/Democrat party lines for acceptance. Almost all Republican Presidential candidates spoke quite frequently of God last year during their campaigns, while Democrats didn't mention it as much. However, in Europe, it doesn't seem to have an effect, other than (some) people's issues with refugees (which happens in the States as well anyway). Why does Christianity affect American politics more than (Western) Europe?
This straddles the line between the 20 year rule pretty intensely but I'll try to answer it while following that rule.
I would say that as early as 50 years or so before the French Revolution, and certainly afterwards, religion and state were becoming increasingly separate, culminating in that being a critical point within the French and American constitutions, and where the USA underwent the second great awakening, Europe never had such a resurgence. That's the earliest beginnings of this separation that I can recall. Later, demographic shifts and higher educational standards began to remove religion from European society, as early as the 1980s there even began to be some talk of a gradual dying out of religion in Europe entirely. This decline has not lended itself to any benefits coming to those within politics who make religion a big deal. Particularly in France, even showing your religion off in public has become something "un-French" and unprofessional in the same way as an openly gay politician would be treated in the USA.
Here is a similar thread: https://www.reddit.com/r/AskHistorians/comments/19isi7/why_did_europe_become_less_religious_over_time/
Aren't there several European countries where abortion and gay marriage are illegal? Is OP correct that the US is more religious? Shouldn't this question be why do the republicans mention religion more frequently than the democrats?