When talking to new people with romantic interest, how far do you allow that person to bend your beliefs, morals, etc.?

I ask this question because I feel many would easily say they don't get bent, but for some guys this is a huge problem, actually I'd argue it's what separates guys from being strong or weak.

The problem I'm describing is how long a guy is willing to run with a girl's issues or "reasons" why 2+2 doesn't actually equal 4. Sometimes there are valid reasons, but for the most part it's some other-worldly problem that always seems to be the major barrier that halts you from advancing where you want to go.

It's always hard for me to tell, because I'm an extremely gullible person, whether or not I'm being too harsh, or whether I'm being played for whatever emotional solace the said girl is getting, especially because some girls are far more dramatic than others.

Anyone have any advice on fixing this? I'm assuming I should just be more in-tune with myself and trust my gut feeling on most of this stuff.