My DH has high bp, same situation as your DH. It's genetic (he also had 2 stents put in 6 years ago). He takes a very low dose (5-10mg) of a BP medication that is not a beta blocker. It does not affect his riding at all. There are lots of medications for high blood pressure and many have been around for years, so are well tested. You may be thinking of beta blockers, which lower your heart rate and suck for athletic people to take. My DH's cardiologist wanted him on one after his angioplasty, but that lasted about 2 days, since DH's resting HR is already super low. It's more for people like our friend, who had the same surgery as my DH, is still 50+ lbs. overweight and never does any exercise.
Unfortunately, being athletic does not always protect you from these things.