This may come out a bit more bluntly that I intend it to, but have you (or mum) tried genuinely and politely asking the FC directly why he's wearing tights and having a conversation about it? It'll probably get better results than this back and forth with the SW, and it might even be that mum or you could give the FC some advice.
-It might be that it's to stop his nappy leaks (as you've mentioned he's 4 and still in nappies)
-It might be to actually prevent him being teased (you've mentioned several people think he might be teased for wearing tights, but to be honest I'd think it'd be more of an issue for him to be teased for still wearing nappies at 4, if he gets changed and is wearing tights, they're what's visible, but if its socks, the nappy would be too)
-It might be because he actually picks them out himself (and you may be able to work out if there's a reason for this that could translate to other clothing)
-It might be because he's shown more interest in them than socks, and FC finds it easier to get him to wear them or keep them on (which may be different to mum's experience)
-It might be because he is genuinely cold in the FCs house, or they spend a lot of time outside
-It might be that he's got sensory issues with the jogging bottoms that have come to light due to the recent changes in his living situation, so the tight alleviate them
I think the way the SW has gone about this is very wrong, and her concern about it being a girls item of clothing is something it's fair for the FC to ignore, if it'd been about a pink tshirt for example, but it was his favourite, you'd probably be hoping the FC did ignore the SW.
A better way to raise it may be to speak to nursery directly and let them know what you've seen in terms of him seeming too warm, ask if they've seen it too, and ask that they let FC know that 'he usually seems too warm, and they often have to remove his tights are nursery as he's going red and blotchy, physically warm to touch etc. So could he please be sent with socks, or generally cooler clothing in future, if he needs to wear tights on the way due to staying warm on the walk there's room for him to get changed there' Then you can mention to SW that you've noticed that the clothes he's wearing means he often seems too warm, so you've mentioned to nursery and asked them of request FC dresses him in something cooler as they'd noticed it too.
If it turns out he's super keen on the tights, then could you suggest he wears something different over them, so the tights are his main layer, shorts, skirt, lightweight trousers etc? I also think this would go someway to reinforcing the point that it's not the tights you're concerned with, but that he's wearing too many layers which is making him too hot.