I had a discussion at my gym about this the other day - their rules are 8+
DS (11) went into the male change after swimming, as usual and I obvs went to the female.
He then proceeded to wait in reception when he'd finished for me to come out of the female change.
When I came out of the changing rooms I got taken to one side and told that he shouldn't be sat in reception by himself and that under 16's need to be supervised at all times - but she couldn't give me an answer as to how I do that without him coming into the ladies with me or me going into the men's with him 🤷🏼♀️ (I'm not saying he should be coming in with me, he's too old, just stating that's the only way I could supervise him in the absence of family change facilities).
The young lady then suggested he sit in the men's changing room to wait for me to come out so I asked how he was supposed to know I'd come out into reception if he stayed in the men's and why he was ok unsupervised in the men's change but not in reception and she just responded with "well, I can't see him in there and I can in reception".
I asked to speak to a manager to iron out what I should do (not rudely, just to ask how we sort it given we're tied into a membership that he wouldn't be able to use if we couldn't sort it) and the manager immediately said that of course he can sit in reception and wait, why wouldn't he be able to.
The young lady wandered back behind reception saying ti her manager "but he can't be unsupervised" and wasn't getting that he would be unsupervised in the male change regardless so might as well sit in reception so he could see me come out. Gave me a laugh.
Anyway, 7 isn't too old to be in with you, I don't think there is a definitive age, more when you feel they're sensible enough to wait elsewhere or use the men's etc. I started with DS by nipping to the loo myself and asking him to wait at our table etc, then started letting him go to the men's while I wait outside and then letting him go by himself and come back to the table himself etc.
One thing I found was that he needed to be able to get himself out of toilets by himself - our cinema, for example, has really heavy doors that he couldn't open by himself at first.