Other games (Battlerite is the one on my mind) leave the "casual" and "ranked" queues separate, but track rating in each mode separately, and allow players to be matched cross-queue. When a team of Ranked players meets a team of Casual players, the Casual players don't see the Ranked players' ratings, but the Ranked players see the Casual players' "hidden" ratings, and are matched with them accordingly.

In that kind of a system, Ranked vs. Casual is "please show me my rank" versus "please don't bother me with that shit", and even for players who are invested in their rating, you get to choose "I'm playing seriously" versus "I'm learning a new job, trying some weird stuff, or otherwise not at my best". In the games I've played, it seems to work pretty well, and insulates against the occasional unfun shitstomp in a mode with no matchmaking algorithm whatsoever.

Just don't bother people about rating if they don't (or shouldn't) care about it, please.