NextDNS connection trouble on iOS devices

I have plenty of devices from Windows, MacOS, Android and iOS/iPadOS in my household. All of them are configured to use NextDNS, but I experienced consistent issues with iOS/iPadOS devices. Sometimes they work, but after a while of no usage the connection will get stuck (Safari progress bar not moving, chat not refreshing, video not streaming etc). The only fix is to disable NextDNS to make the internet go through.

I tried to use both profile generator and NextDNS app, both to no avail. Same profile worked on all other devices, so I don't see the problem is on my ISP or WiFi. I'm thinking that probably those Apple devices are operating on different ports that is blocked, but I'm not sure how to find it. Any help is appreciated.