My DDs are in their twenties. When they were starting school, TAMBA came out with research that twins did best in schools where the parents were happy, and that blanket policies of either splitting them up or keeping them together were not helpful. I would say that the school not involving you with their decision, from the start, is a red flag.
My girls were dressed differently from the start, had different hair cuts, one on one time, separate sessions at playgroup, separate dance classes (that one nearly killed me with all the driving). They had different uniforms through primary but this wasn't possible in secondary. They are identical but are not exactly the same to look at. They have been in classes together, been split in school activities because they are twins instead of interest and ability like all the other children. Sometimes they have been together and it has worked and sometimes not, and the same with being apart.
It very much depended on the state of play at that given time as to whether it was a good thing or a bad thing. Teachers are very variable. We have had amusing moments when a teacher has taught one, then wondered why they were still there in the next class
. Not so amusing moments when one was cornered by the music teacher in the first term for not going to a band rehearsal - she played the piano and did not know WTF the teacher was going on about, nor who he was
. I have parents evenings where teachers just tell you what is the same about them
even though they are teaching them in separate classes. I don't think the drama teacher could get herself over it
. It is a breath of fresh air if you get a teacher that just deals with them separately, or totally separate teachers who have never seen the other twin. (Parents evenings were a mad nightmare of rushing around). However, most teachers are very sensible and have their head screwed on and have no problems. Sometimes it is better if they are in the same class as the teachers stop seeing them as clones and see that they are different people. If a teacher only knows one, sometimes they treat the other as if they are the same person when they see them.
It is long and complicated, and school is not forever. You need them to have decent academic results and a good healthy lasting relationship, which is forever.