Rehearsal Dinner invites

If the officiant is attending the rehearsal, I would also extend an invite to them for the rehearsal dinner.

It is always polite and customary to extend an invitation. Unless they are a very close friend, they will decline.

Yes, invite. They will likely decline.

I would invite them

Typically yes. If they're not super close with you then they will probably decline

If they are clergy, or friends, invite them. If they are hired by the event strangers, no. Sometimes such strangers don't say no, and charge you 2 hours, so that essentially they see it as work. I know people who have invited their JP and been stunned to get a 40% higher total bill.

I’d invite them if they are attending the rehearsal run through! Most of the time they probably decline anyway