I drink coffee daily, normally two large cups, once in a while I'll have a third. I haven't seen any differences related to drinking caffeine, and I don't remember any mention of related issues in the HRT information package I received and signed.
Must like anything you ingest, if the quantities are unhealthy for you while on HRT, they would have been unhealthy for you if not on HRT. My layperson's understanding is that as caffeine is a diuretic, too much could affect your potassium levels...and as Spironolactone affects your potassium, well you see there is a connection which would need to be monitored.