The question is "Why they THINK they are going against their conscience"
probably because that is what they have been taught.
It often is easy to convince someone to take on a new belief (ie Death penalty, abortion, war, ect)
The situation is often many people do not look at all 3 sides of an issues.
Its easy to make one statement and people just accept it.
For example- Recently Sen Schumer (NY) stated that if the MAGA R's get their way - no one will be able to get an abortion
in the USA. But he did not mention that many States/Commonwealths will still offer abortion.
At least 20 States/Commonwealths would have full access well several more would only have restrictions.
Map: 23 states would ban abortion in a post-Roe America
Going back to the military Alvin York did not believe in killing people - but after several lengthy discussion with his commanders, he ended up being awarded the Medal Of Honor - in part for killing a large number of the enemy.