Look - in "natural" scenarios - by "natural" I do not mean that they are in any way better!!! - I mean...

...so imagine a house that is staged for sale

...now imagine a house that is being lived in...

In a house that is staged for sale things are all orderly and arranged to please the eye.

In a house that is being lived in, things are a little messy, at times, and are not arranged so much to please the eye but, to are arranged in a way that reflects how objects are being used.

So a dating site is like a staged house. And if you meet a person off a dating site, then, chances are, he won't know anybody from your natural social circle.

Meeting people "naturally" - meaning, in the course of ordinary living and not off "staged" dating sites - very often results in situations that are a little messy, such as the one you are describing, when men and women change partners while remaining within the same social circle. As a result, a current boyfriend might be or might have been a friend of an ex boyfriend. All of it is entirely normal and, to me, much more interesting in terms of complex relationship dynamics than the "staged" environment of dating sites. I would encourage you and your boyfriend to talk more about it, and, in particular, to explore why he feels awkward. What is underlying the awkward feeling? This question might have a number of reasonable answers - which one would your boyfriend give? It is worth asking.