Not when used for big dramatic emotional breakthroughs, but when used for silly little mistakes. Example: you apologize for loading the dishwasher incorrectly, or leaving your socks on the floor, or interrupting someone and the person responds “It’s okay; I forgive you” in a non-joking way. Any time I hear, “I forgive you” in these contexts, it seems like such a sore winner kind of response. It doesn’t seem gracious; it feels condescending, like the person is doing a grand favor by overlooking your minor mishap.
I’d prefer just “okay” or “okay, thanks” or “I get it” etc. That’s what I say if I’m the wronged party in these minor issues. Am I super crazy and oversensitive? You can say yes!