Caffein in tea and coffee apparently causes spikes in blood pressure after drinking these, and also apparently some people who drink a lot of these suffer a permanent blood pressure increase. I doubt if this is much of a guide but, because since my youth I have disliked both tea and coffee, I drink neither but on the other hand, my wife drinks both although certainly in moderation. She is on blood pressure tablets whereas I am not - I am three years older. However, I should mention that high blood pressure runs in her family and not mine.
Probably, if you are likely to develop high blood pressure (genetics, weight, health issues, etc.) then caffeine consumption is not an advisable. For the most authoritative answer consult a specialist.