No need to turn off Next DNS - I have it turned on on my router at home.
You just need to whitelist the servers we use for redirects:
twit.tv (TWiT)
chtbl.com (Chartable)
pdst.fm (Podsights)
traffic.megaphone.fm
From time to time various blocklists block these. You can choose the blocklist you use on NextDNS. Or just whitelist these URLs.