Friends of opposite gender ok to have after disrespect, hurtful disloyalty?

I need some opinions please just to get what others think about this situation.

Let’s say you’re in a relationship that’s going on 2 years and the person is living with you, has been actually for over a year. Now about 9 months ago, you learn that the person you’re with had been flirting, sexting other women the entire time. From before the moment you met to when you caught him. On top of, constantly messaging a former best friend of yours bashing u, and declaring love for her n not u n are with you cuz he can’t have her. Now, after you learn all this, see all the photos and read all the messages, you fight, he declares he’s sorry, he was stupid, he didn’t mean any of it and that he will do whatever it takes to make up for it and fix the trust damage as best he can no matter what it takes or how long it takes. You agree and give one chance. You wanna see if he’s for real. So part of the stipulations were no secrets, access to everything if asked and open n honest, If he gets contacted by any female or if he contacts one, he needs to tell you. He also needs to drop from his phone and online profile, any female he’s been inappropriate with during your relationship. Because sadly, u discover a few you met recently at that point were some he was hitting on. Days after that fight, you discover the photos he had of other women, he deleted out of his phone but not before he forwarded them to his email. And, he did clean up his friend list on FB but not thoroughly, for some girls still remain and to this day are STILL on there since you brought it up a few months ago.

A few months later, you see he wasn’t sexting anymore or that you could tell but did see he was browsing the photos of some other women he supposedly cut out for you on their profiles. You saw that on his phones web history then noticed that night after seeing it, he deleted the history.

Then a few months ago, you discover he emailed a few females who’ve yet replied and helped another fix her car and give her a good deal on it. You overlook it because he said the emails were to a former co worker and wanted to see if they were hiring where she is and he simply forgot to tell you about it cuz he’s so busy at work, and the one he helped, he was gonna tell ya but you hit him up n found out before he could due to her FB update that same day.

Last week, you discover not only has he deleted some text trails on his cell phone but also he hit up another female and also tried to get another friend of the female friend he hooked up at work a job at his place of business, and he hadn’t told you about it. So you bring it up. And he gets angry, telling you he knows he hurt you and traumatized you but you need to let it go. He should be able to hit up friends just to see how they’re doing without a problem from you. You should trust him and that he’s not doing anything bad or wrong. And ends the night with that’s it, he’s over it. He’s done. And goes to sleep.

What are your thoughts? Is it right for him to hit up females he doesn’t talk to anymore or for a long while with “Hi” texts and “Hey stranger how ya been?” messages? I don't believe it is and I believe this guy still hasn't rebuilt any trust let alone be okay to have girl friends with no issues about it.