Having once been a conservative Christian, I know what it is like to feel pressure from outside sources ("the world") who didn't tolerate my belief that it would be wrong for me to make a cake for a gay couple (because "gays need to repent of their homosexual lifestyle", and many Christians have various personal, social, and political reasons to exclude gay people). At first, it was easy to dismiss pressures felt by homosexuals because I knew I had the truth ("it's a faith thing").
The more I learned about the world and the people in it, the more evidence mounted against my stances (stances which weren't developed in good faith, since they were rooted in fear, guilt, and shame from a very young age, and were copies of the traditions and opinions of others). I realize after the fact that I was in an impossible position; that I could not keep honor the evidence or people I knew (or even myself) AND maintain my faith (because it din't jive with reality).