My BB had become a touch loose on the drive side, allowing the BB mounted chain device to rotate easily, so I went to tighten it. However, I found that it woultdn’t tighten. It would get to almost the pinch point and then just go slack again. If I removed the chain guide then it would tighten.

My first throught was that the frame threads were knackered, but I tried a Shimano BB instead and this was absolutely fine. The length of the threads looked to be pretty much identical, but the threads seemed deeper on the Shimano one (and I had to kind of screw the chain device on whereas the Hope cup easily pushed through).

Is it likely that the BB threads have somehow worn down? Or is it more likely that the frame threads have worn and Shimano BBs just have deeper threads? The non-drive side Hope cup still fits fine – I can’t see an obvious difference in thread depth between drive and non-drive side, but it’s pretty hard to tell and I don’t have any callipers.

Has anyone else had issues like this with Hope BBs?

That happened with an XTR BB of mine (in a Ti frame) but the damage to the BB threads was obvious.

I suspect, possibly, you have the same issue I had.
The threads in the Hope bb cup, could be damaged, which might be why they appear shallower.
I found that I had a tiny bit of play at my bb. The drive side cup had worn threads and the frame thread was very slightly worn. A new Hope bb cup solved things and everything has run nicely for the past 1500 miles or so.
The issue was put down to the plastic bb spacers on the hope bb, being able to compress very slightly under load and causing wear over time.
This made some sense to me and was suggested as a cause by my lbs and also considered a ‘ possibility’ by Hope who provided a new cup . The replacement was fitted using metal spacer washers.

EDIT… By the way I had zero bearing damage and all had been fine for the preceding 18months.

Sounds like BB thread wear may be the issue then, although I’m not using any plastic spacers, just the aluminium Gamut chain device plate.