I think you're being harsh OP. They are young and assuming you're in the uk, have hardly had time to socialise in the last 18 months! The behaviour you're describing is hardly unusual.
I think you need to change their mindset. Some kids dont enjoy going to clubs. You're worried they are going to miss out, but being forced to spend time doing something you don't enjoy isn't enjoyable. I think that age is still young for clubs. My 6 year old is average in the shyness department and she tried various clubs and activities but until recently has been too young to really get that you need to commit to something and work at it before it becomes enjoyable. She has only just finally found something that she likes. Before this she was always too knackered from school and wraparound as well.
A few other things that you can do to help them -
Dont use the words shy infront of them or about them. It's clear you think it's a negative thing. If someone else says it, correct them 'oh is Jonny a bit shy?', you say 'he just prefers to watch for a while and take in what's going on before joining in'.
Build their confidence about being quiet. There are good points about being 'shy' like being able to entertain yourself, being a good listener etc.
If they say they dont want to go to a club, listen to them and find out why. Is it because they're not that interested in the activity? Let them choose a different one (eg a club but for people doing an activity solo like crafting). Is it because they are not sure what the teacher is like or the premises? If so ask if you can meet them briefly one day and have a look around. Is it because they dont know anyone there? Then find one that their friends go to. Is it because they dont want to stay the full hour? Then arrange to go for shorter time periods and build up. Is it because they are worried about being away from you? Then agree you'll wait outside and come and get them if they ask the leader. It might be at the moment that they are overwhelmed with starting school etc again and need to get used to that so ask them to consider joining something at half term
But forcing them to do something that they don't want to do, and acting like it's some sort of character flaw, will only backfire