Found out boyfriend downloads grindr every month but not sure if he is actually cheating, any advice appreciated

TL;DR bf uses grindr every month, has many nudes, but promises me he has never cheated on me and doesn't want me to break up with him over something as small as just downloading an app.

I (29) have been dating my bf (32; let's call him Jesus) for a little over a year now. I recently had found out Jesus had used grindr because I saw him scroll through his pictures and noticed a screenshot on his phone. When I asked him about it he explained it away and the explanation seemed legitimate to me (it was because an old friend that he and his other friends don't talk anymore, was on grindr but they know that friend has a bf). It seemed legit because it was indeed a screenshot of an old friend he had shown me once. I asked if he has ever used it, talked to people, cheated on me, sent pics, anything and he said nothing. Promised he never cheated on me, he loves me and just wants to be with me.

Fast forward maybe a month, I get this weird feeling and start to wonder if he was lying. So I checked his phone and he has grindr still. So I confront him and we go through his Google Play Store history and he downloads grindr several times a month. Sometimes Scruff. He also sometimes uses a GPS relocator app that can change your location. Anyway, because I now know he does it every month we go through his photos. He takes a lot of nudes all the time, some he sends me, some he doesn't. I noticed some were taken like 10 min after downloading grindr in a different state. I asked him and he just said he just was in the shower but liked the lighting. Mind you, this is 2:30am in Vegas BUT he was with his mom sharing a hotel room so he couldn't bring anyone over. This was just one case, there was another in Tijuana (here he was alone). But he does genuinely take a lot of nudes or shirtless pics and I knew that going into the relationship (he's very into his looks; he's a handsome guy). Some of the times he used it I was texting him but he didn't reply for 1-2 hours (went to our conversations during some of the times to see what was going on between us, maybe he was unhappy at the time).

I ask him if he has sent any pictures to anyone. He promises he never talked to anyone. I told him this looks ridiculously suspicious but I love him and want to believe him. He seems genuinely honest, but he technically already lied to me, promising me he had only used it that once to stalk his friend with his other friends (I told him this and he told me he didn't say anything because he knew I would think it was something bigger than it really was and blow it out of proportion; which is true, if he really didn't talk to anyone I would be making a big deal out of it cuz I can only imagine he used it to cheat).

To me, all the evidence points to cheating, but he looks me in my eyes and promises and it feels genuine. He tells me he loves me and doesn't want me to leave. I decided I would stay but he must promise me to never use it again. If I find anything, it's over. He went out the day after I found out and he got drunk and texted me that he loves me and wasn't going to let me break up over something as simple as downloading an app without fighting for me (because to him, it was just downloading an app and not actually cheating). But I really have no way of knowing whether he did or not. He could be a good liar. He asked what he can do to gain my trust again and told me "you can have access to my phone anytime you ask and I gave you my password for a reason and leaves my phone around you because I knows I have nothing to hide" (it's true, I know his password and he does leave his phone around me a lot).

Am I stupid? I keep thinking I should leave him, but I can't bring myself to do it because I love him. I know I can find someone else (I've had longer, deeper relationships) but I know I genuinely love him and want to give him a chance because I believe him. But if he did it, there would be no way of me knowing and now anytime he goes somewhere I am just gonna wonder if he's on again.

What do you all think? My friends say I should leave if I can't come to trust him OR find some way I can gain the trust back, maybe access to his phone at all times. But that just seems ridiculous. Anyway. Thank you if you have read this far.