As everyone else has said, this is a pretty normal hangup, and if it’s really where you plan to live for the foreseeable future, only time will wear down the edges of that anxiety. It sounds like your parents raised you to be very open and you have an honest relationship with them and open invitation to live with them until you find a path that takes you elsewhere. Frankly, that’s great. My own daughter is a pre-teen but honestly I think we’re on a fairly similar path, but that’s more because it’s what feels like the right thing to do and the right way to treat someone, compared to the arbitrarily rigid households my wife and I grew up in. It doesn’t make make it magically not-alien.

It’s only been a month and he likely grew up in a different style of household. Honestly, in the US at least, the communities that most commonly do multi-generational living are very much not the ones okay with unmarried partners staying over. That’s a pretty significant cultural disconnect, and it’s going to be a while before he gets over it and truly believes that your parents are as okay with it as you claim. It’s probably going to require them to be almost comically over the top about it being okay (which has its own social hazards, LOL), or else it’s going to require baby steps. A trip together could help, as someone else mentioned. Or, a movie night that runs long and he stays in a spare bedroom. Eventually, with exposure and with a relationship between the two of you that proves to be solid over time, he may come to feel that it’s less awkward or disrespectful. He might also be a bit (overly?) self-conscious about the slight age difference in front of people whose primary job over the last 20 years has been keeping you safe.

So yeah, he’s sort of bringing his hangups into the relationship in a way you likely find frustrating, but I wouldn’t worry about it, certainly not until it’s been a good bit longer. It’s a common thing, coming from an honest place (and as mentioned, anxiety+expectations could create a lot of issues around the very intimacy you want to promote). In the meantime, it’s fairly easy to work around, especially since you do have the kind of relationship with your parents that makes staying at his place unremarkable. Eventually, yes, he should grow to trust you and your parents enough to believe you all when you say it’s fine, and if that’s still not enough then to have the kind of open conversation with you as his partner to understand why it’s not going to happen. For now, just keep doing things to make him comfortable at your place, but for the most part I’d let this one go.