I wouldn't loan it out to walk away aside from a select few, but hitting some balls with it or sharing a cue while we played together is fine.
"Who do you let play with your cue?"
Anyone who wants to.
I don't understand what the big deal is.
It's a piece of wood.
Long as I'm standing there anyone can play with my cue.
I even offer people I've never seen before if they want to try my cue when they come over for a chat.
I don't actually let anyone shoot with my cue. I am sorry if they are offended if they ask and I say no, they should know better then to ask. That is not to say I would not let someone hit some balls with my cue, but borrowing it to play, "NO".
Very few people use my playing cues. I let a teammate borrow my cue once and he slammed the shaft against the edge of the table after he missed a shot.
The last time anybody other than me used one of my cues was when I let the owner of a local pool hall/restaurant hit some balls with it. Some random guy in a pool hall - zero chance. I put my cue on the next table while I broke with a house cue and in just the time it took me to break a guy two tables over had walked over and picked up my cue and was examining it. He never said a word to me while I was holding the cue, waited until I laid it down. I immediately grabbed the cue back from him.
Look at it this way. Who would you let drive your car?
I have a piece of wood that I let people borrow, it's a $50 McD Star cue.
Luckily no-one that used any of my cues has damaged it yet I all the years I've owned cues.
The most issues I have is with random people grabbing the cues thinking they are house cues or sticking them up on the wall. I actually had a group of kids look at me like I was some random crazy guy when I walked over to their table to take my cue from them after some girl in the group grabbed my cue. Some people seem to think that any cue in the room is a "house" cue for the taking. I wonder if there are people that don't even know you can buy your own cue or that there are cues out there that cost more than $30.
I would let someone drive my car but not my cue.