Hi, as a former teacher, no, I do not think that it is unreasonable or 'too strict' to make children wear a borrowed kit for P.E. if they forget their own.
IF a parent sends a note stating that the child is unable to do PE then they will sit out the lesson, usually with some work to do in a.n.other classroom. Class teachers do generally check in case the parent has forgotten to write in if a child comes without their kit and expecting not to take part for a health reason, but teachers do keep spare kits and it is an expectation that all children do take part if they are well and able.
There are children who dislike P.E. who will purposefully forget their kit / hide it to try to get out of taking part. Sometimes children feel self conscious about getting changed in front of others and culturally, i.e. in the travelling community, we are sometimes asked to provide separate changing arrangements even for young boys and girls. If a child does want to change in private i.e. go to the toilet area, this can be facilitated.
However, P.E. and the health benefits it brings are seen as very important and the government requires schools to provide 2 hours of PE at primary level every week.
I am always surprised when parents do not encourage their children to do PE, but I think it is right that schools actively work to facilitate every child being involved.
If you have a child who is reluctant to take part, then the reason/s why should be investigated.