You can't turn off the out of space message, instead you will need to manage your iCloud storage space.
To manage your storage first find out what is stored in iCloud. Settings > General > Storage & iCloud usage > Manage Storage.
Backup size to iCloud storage usage is not a 1:1 relationship as your question suggests, I.e. 128gb of iCloud storage is not needed to backup a 128gb phone. Music and Apps are good examples of items not included in the backup.
Photo's and videos are stored in your iCloud space but as part of iCloud photo sharing, not a "backup". As your question suggests this is the largest use of space on your phone, you might want to switch off iCloud photo sharing (settings > iCloud) to save the space. Another good solution might be to switch this item off and download the Dropbox app, and let it backup photos and vids.
Another iCloud space waster might be old device backups. A new device won't overwrite the old devices last backup. When that backup is no longer needed it must be manually deleted.
"default+$5 20GB iCloud plan" makes no sense, you likely either have free 5gb plan or the next level up is 50gb for 99cents a month. 5gb should be plenty to backup your 128gb phone, if you turn off iCloud photo. My 64gb phone is at about 52gb but my backup is just 1.6gb after compression and subtracting what's not backed up as part of a backup.
In summary, and to directly answer your question. No you can't turn off the out of space errors, you must manage the use of iCloud space instead.