I have OpenWRT set up with DNS over HTTPS on the router. This works quite well.
But also have Private DNS on my Android cell phone. This Private DNS is a DNS-over-TLS server. My cell phone can't access Private DNS when connected to the OpenWRT router.
The same cell phone can access Private DNS very easily on other networks, both mobile and wifi.
I also have a laptop with DNS-over-TLS. The laptop also cannot access DNS-over-TLS through the OpenWRT router.
For testing, I disabled the firewall on the router (service firewall stop). I still couldn't get through with DNS-over-TLS. I'm not sure it's the firewall that's blocking the requests.
it was actually hijacking all traffic on port 853 that is it was preventing all connection forwarding to wan over port 853.
in other word all the connection over that port didn't go to wan directly.
and the https-dns-proxy was designed to listen for clear dns over listed ports. as it was encrypted the proxy just didn't recognize and dropped it. and the private dns didn't get right answer.