This app was mentioned in 3 comments, with an average of 1.67 upvotes
ServeStream is a streaming music player for internet radio. Free and open-source.
After TuneIn became evil and added ads to their paid app, I've searched hard for a simple music player that can open three radio stations I'm listening to, and supports .m3u with network stream URL inside.
At first I've used Online Radio by Bitcraftr, but it does not support .m3u and is not developed anymore. ServeStream is newer and with less bugs.
Another option is to open .m3u file in VLC, it plays network streams fine, but is not very convenient.
And Poweramp supports everything but is a paid app, I did not buy it because I've cheaped out after TuneIn flop.
ServeStream is another one where you can enter the URLs for each of your radio stations: https://play.google.com/store/apps/details?id=net.sourceforge.servestream
Put your list into m3u-playlist and you don't have to add them by hand.
Not sure if it works with every stream out there, but since you have the URLs, it might work for you.
Editing the master file database of TuneIn might not be possible, since that's updated through the cloud.
I would like this feature also, and probably pay money if it was worth it. I found this app to listen to streams https://play.google.com/store/apps/details?id=net.sourceforge.servestream&hl=en