First - I don't think it's an age-related thing but it's very difficult for anyone to go to something that's as established as Sidmouth and instantly feel part of the groups that have been going for decades.
I think big festivals work best if you go primarily for the concerts. I don't think going with the expectation of "becoming" part of the fringe on a first visit is realistic. Perhaps, with age, I've just got the hang of waiting a while in order to be accepted but when I go somewhere new, my first visit is usually just to find out more about it - not to expect to be a part.
As far as Sidmouth goes, there's so much going on in the fringe-type events that it would be easy to miss some of them – perhaps the ones that would best allow you to do something yourself. If you want a stage, sign up for the Dukes open mic. If you want an almost guaranteed chance to sing (with or without an instrument), go to the daily morning singarounds (run by Kitty) at the Royal York & Faulkner or to the evening ones (run by Rosie or, this year, Dave (Acorn4)). For unaccompanied singing go to the Anchor "Middle bar". In all these cases though, be prepared to be there for up to an hour or two before it's your turn. They're not run on a "favourites first" basis but they're all popular with lots of others there waiting too. You're more likely to get a song in sooner at the "Newt" but again it'll depend on how busy it is.
There are programmed places you could try like Colin's themed singarounds in the Rugby Club but, again, be prepared to wait. I've sat there for an hour or so without being asked to sing (and I know Colin) before having to move to get to a different event but I never thought it was anything but the luck of the draw. (I did give his book a good review!) The Ballad session (traditional ballads only in the main) in the Woodlands rarely has enough time to get on all those who've signed up – though you'll get on early the next day if you get in early and sign up.
I've only been to the evening "Folk Club" in the Arts Centre once but I think, a bit like the themed singaround, if you sign your name and are prepared to wait, you'll get your chance eventually.
So there are plenty of opportunities but you do have to be patient as they're all popular with lots of people wanting to sing.
The Volunteer is, as others have said, not a singaround. In the main the same people go each day and each year so it's bound to appear cliquey if everyone knows each other. An MC invites people to sing and you either have to be known to the MC as a singer or, presumably, be quite pushy to get noticed. That's because it's there, in my opinion, as a showcase for the best of what's on offer at the festival so a certain amount of quality control is needed. There are other places for run of the mill singers such as myself or for those wanting a chance to become more well known.
There are plenty of other places where singing happens but they tend to be created where groups of friends get together so they're bound to be a bit more cliquey. The central group in the front bar of the Bedford all seem to have been meeting up there for years, groups of friends go to the Swan and start to sing but I don't think they're there as a platform to bring new performers on – they're just friends enjoying some time together.
Sidmouth is a big festival with lots of guests and concerts. It does have a very active fringe but I'd guess the organisers are more concerned with the former. If your interest is in the traditional side and you want more participation why not go to some "song and ale" style festivals to get yourself more well known and get the feel of things a bit more?