FaceTime doesn’t show as option for some contact

I can FaceTime some people in my contacts, but not others. In the contact listing of those that don’t work,  the FaceTime option is grayed out, but shouldn’t be. In response to suggestions that you may have:

— I know these people have iPhones

– they are marked as favorites

– I’m in their contacts and favorited (some)

– I’ve deleted and created new

– have both closed app and restarted phone

– at least one is able to FaceTime me, and I can FaceTime them back by clicking on their name in the call history. When I do that, my number shows for them, but not my name.

– two are my parents, I know that one of them has an iPhone 5 that was previously used by Verizon, but unlocked. Another was a new SE started with Consumer Cellular. The 5 is also on CC. (Separate plans)

I don’t think the carrier is the problem because I used to be able to FaceTime with my mom.

Please help. One reason we got them iPhones is so we can FaceTime with them.