I don't think your experience is limited to gay relationships. Tinder is more or less the straight version of Grindr, and a guy or girl could just as easily be on there while in a relationship (though guys tend to be more hook-uppy in general). You did nothing wrong in expressing your fears and concerns and he should respect that. All you can do is be honest and open with your feelings. There is no right or wrong answer to this, as each couple has to set their own boundaries.
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The part about him forgetting to delete it sounds like a lie given the rest of it. It sounds like he's keeping some options open, whether that's just for sex or a b/f he likes better I could not say, but if he was into you only and forever, we wouldn't be having this conversation. Porn is easily available on the Internet so there's something more to this.
I think you have 2 choices: either dump him because he's still browsing (and if he's not sampling yet, he's still thinking about it) or try to get on the inside, find out what his real fantasies are and try to be a part of them. That last part may not be possible if he's addicted to new experiences ("strange"), which you will never be again, but who knows.
How long have you been with him?
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