WIBTA for refusing to meet my GF’s ultimatum?

Hello, throwaway account. I just need some perspective, so here goes.

I (28F) moved in with my girlfriend (29F) about 9 months ago when they asked me to. They own their own home, whereas I was renting a room from a coworker/friend, so this makes the most sense. At the time, we agreed I would not pay rent (GF’s idea) because (1) I am not on the mortgage and they didn’t want me to feel like I was paying for their asset, and (2) they make more than double my income and don’t need the money. This was purely a decision based on wanting to live together, not for financial benefit. I was even happy in my previous living arrangement. So truly just for the sake of being together.

That said, I of course do benefit from the situation, as this frees up a lot of my income. I am extremely grateful for this. One way I try to show this is by being the one to pay for all the fun stuff. Obviously we aren’t like eating out every night or anything, but I do spend a large percent of my income on us doing stuff together that we probably would not otherwise do.

The other thing you need to know about me is that I have several jobs, all part time, which add up to about 40-50 hours a week of work (relatively average), although sometimes those hours are on weekends. There is one job in particular that tends to schedule me for Saturday or Sunday. Well recently my GF told me that they want me to quit that job because they hate that I am gone on the weekend. The problem is, that’s my favorite job and I would be really sad to quit. When I told my GF I didn’t want to do that, they said that in that case I should be paying rent. When I asked them to explain how that is related, they told me it would prove I’m dedicated to the relationship.

I feel torn. On the one hand, I understand GF just wanting to spend more time with me. And I understand that it’s not exactly “fair” that I get to live here for free. On the other hand, I can’t help but feel that explanation doesn’t really make sense and I feel uncomfortable with my partner trying to push me to do something I don’t want to do in this way. And I don’t want to set a precedent that I can be told to do certain things with my life because of living here for free. We had an agreement, and it’s not like the have had some kind of life event where they really need the financial help. But maybe job/schedule is the kind of decision your partner should have input on? I don’t know.

WIBTA if I just put my foot down and said I won’t be paying rent or quitting my job?