It's not weird that this bothers you, and it's also not automatically a red flag - context matters way more than the fact that contact exists. Some people genuinely stay friendly with exes, especially in smaller social circles where mutual friends keep popping up. If they're only texting about those mutual connections and not constantly messaging at 2am or making plans one-on-one, that's pretty different from someone actively maintaining an emotional relationship with their ex.
The real question is whether you trust your boyfriend, and whether his behavior gives you actual reason not to. Does he hide the messages? Get defensive about his phone? Spend hours texting her while ignoring you? Those are concrete signals something might be off. But if he's being open about it, you can see the messages are casual, and there's no secrecy involved, then you're probably dealing with your own discomfort rather than his behavior being the problem. That's still valid to feel - plenty of people wouldn't like it - but it's different from him actually doing something wrong.
If it keeps eating at you, talk about what specifically bothers you instead of asking him to just cut contact. Is it jealousy? Fear he's comparing you to her? Worried he has unresolved feelings? Once you know what's actually driving it, you can figure out if this is something you need to work through or if you two just have different comfort levels and need to find middle ground. Either way, calling you paranoid isn't the move on his part - your feelings deserve to be heard, even if his actions turn out to be completely innocent.