I can imagine they might in a school for swimming. When you get changed for swimming you get fully naked so it is different to getting changed for P.E. It's one thing for a mother to take their son into the changing rooms at a public baths, where he is supervised by his parent - but for teachers to OK it may open them up to complaints from the parents of girls. There are lots of things that parents allow their children to do that teachers cannot allow - even though they know full well that the parents would be OK with it - because of risk assessments and the threat of being sued and fired.
But there is more to that story that doesn't make sense.
That 6yo trans girl apparently goes to a school with a pool. 'school pool' is in the tweet. That aint no state school, cupcake. The parents are paying to send their child there - if they have a problem with the way the school is choosing to respect the dignity and privacy of their female pupils ahead of the identity of the trans one - they can vote with their feet.
If they just meant 'when they go swimming with school' - I've worked in a lot of schools - it is always the year 4s who go swimming. Year 4s are 8/9 years old. If the school is feeling affluent they may also send the y5s (9/10). I suppose it is not beyond the realms of possibility that they might send the year 3s (7/8) though I have never seen it.
But what I have never even heard suggested is sending KS1 pupils swimming. (they have trouble enough getting changed after p.e - imagine trying to get 30 6 year old girls back into their woolly tights when the girls are damp!)
That story is attempting to tug at heart strings - how dare a school put all their girls needs ahead of the one trans pupils needs? But it doesn't add up.