I don't know they ever did try to eliminate Islam, but the particular issue of washing was a conflict between their religious practices. I learned this from
https://tube.kockatoo.org/w/hfsnrYC2aGbr1HEehhwrqZ?start=6m3... by
Premodernist, which quotes and discusses
長春真人西遊記:
> Now the subtext here, which Li doesn't come right out and say, but is kinda understood for a contemporary: when the Mongols forbade people from washing in the rivers, that means that if they caught you going into the river to wash, they would kill you on the spot; because that was a taboo in the Mongol religious system. Now that was a problem if you were a Muslim who had come under Mongol rule, because Muslims of course do ritual washings before prayers, and in central Asia they would very often just go down to the local stream or river to do the washings. But if a Mongol saw them doing that, they would go over there and strike them down and kill them. And there are accounts – not in this account, but there are accounts in other historical works from the period, particularly from Muslim writers – that talk about, it was not uncommon for Muslims to be killed by Mongols in this way.