Account recovery contact set up error re “iMessage”

I’ve repeatedly tried to set up my account recovery contact and I continue to get an error message that says the contact I chose is not using iMessage, which is not true and they actually have me set up as their account recovery contact with no issues. This error message pops up for both contacts I tried to add despite both having iMessage turned on. Please provide instructions to fix this error because I cannot turn on advanced data protection until my account recovery contact is set up.