If joining societies he feels isn’t for him how about a volunteer role/job?
I went back to uni as a mature student and single parent and felt a little out of things, I actually expected things to be far worse than they were but it was still a challenge in the early days.
There was an assumption early on from the younger students that I wouldn’t be interested in socialising outside of lectures/seminars because of dd and being at a different life stage, and the other mature students were a good bit older than me and weren’t up for socialising for a variety of reasons including preferring to socialise with spouse/partner and their usual circle and having elderly parents to care for, but I did a few things that I think helped.
Volunteering to be a student rep
admittedly initially mainly as a “good thing for the cv” but I also really do like helping people. It meant I was in a position to be approached by other students when they needed help/advice on things. I really enjoyed the role and learnt a lot but it definitely helped on social side too, part of it was as there were several of us representing our course and intake and the lecturer & SU member organising recommended certainly in first few weeks that we meet up as a group to decide who would sit on which committees etc. It gets your face and name known and also ime you’re less self conscious because you’re focusing on deciding things with other reps or in solving the problem a student brought to you. Also means you get to know the SU higher ups quicker and they mention you to others too. Highly recommended (and it IS a good thing to have on cv)
Joining societies/clubs that aren’t necessarily focused on the usual type of nights out socialising
Lairy nights out can be fun but they’re not really conducive to actually getting to know people. Plus as I was ltd due to dd daytime groups were a good option for me. I joined a meditation group (which also really helped with all the stress I was under), a lunchtime board games club, yoga group, vegetarian society and the history society.
Certain societies tend to attract people who are more empathic and who are more likely to make sure new members are properly welcomed and included. So I’m wondering if your son has done (as so many do) veered towards the more drinking/sports side of things which tends to be more about competitiveness and superficial levels of friendship.
He could also start his own society/club if there’s something he’s particularly interested in and there isn’t yet a club for it. One of my friends started a comedy writers club and linked it with the stand up comedy society, the writers were clever funny people but lacked the confidence and sometimes I’m afraid ability to perform their material themselves but the writing club was a great success.
being thick skinned and inviting myself along to nights out
This might get me flames! I wasn’t rude about it, but students I got along well with in lectures/seminars/hanging out having coffee between those I started to realise weren’t inviting me along to nights out, as I said they were thinking I wouldn’t be interested. Then one had a birthday and I got her a card and I blatantly said “if you’re going out this weekend to celebrate I’d love to come along, first drink on me of course” and she said she didn’t think I’d be able/interested due to dd. I explained I was lucky enough to have a friend who we helped each other out with babysitting (we’d just do sleepovers at each other’s houses) and if it was ok with my friend I could come... and really the rest was history, that student and I are still friends nearly 17 years later. Sometimes you have to bite the bullet and hope it works out.
I also got a part time job in one of the campus shops, just a few hours a week but as well as a little extra cash it again meant people got to know my face and helping customers out (was the newsagent/sweet shop but I was good at getting in obscure publications for people) creates a positive memory for them. And again you’re not as self conscious as you’d normally be as you’re busy focusing on the job.
Other quieter/more shy students took similar approaches, one of my fellow reps was a very shy chap and actually took the role on to try and overcome this “fake it till you make it” he was a lovely guy, really thoughtful and very practical sort (dad was a builder I think) and so he was great with things like advising students on buying or even finding them cheap/second hand furniture, replacing bust locks, fixing pushbikes etc and I think the respect and thanks he got for helping students with such things helped his confidence.
Another got a job at the student bar and built her confidence through that job.
Also tell him not to be afraid of approaching SU/reps and asking for help with this - It's VERY common and it's what they're there for! They won't mind in the slightest and especially if they're 2nd/3rd/4th years themselves they will know more of what's available and who to put him in touch with (they also KNOW which are the shitty cliquey clubs 
and to be avoided) he doesn't have to suffer in silence, but yes a certain level of perseverance is also needed from him.