One aspect about telepaths that's arguably an open question is whether human telepaths exist in the 23rd and 24th century?
TOS' "Where No Man Has Gone Before" is canon, and it establishes that by the late 23rd century, there are human telepaths and they've even worked out an "ESP" scale to measure people's abilities. However, that's usually treated as "early installment weirdness" (e.g., at that point in TOS, the names "Starfleet" and "United Federation of Planets" hadn't even been invented for the show yet) and something that's been retconned out of existence.
I'm sorry this is like telling a species with auditory organs to switch off their ability to hear. Imagine if in Trek the Enterprise met a race of people who were naturally 'deaf', where sign language was the norm. They would not even consider their ability not to hear a disability. Imagine meeting someone like us, with our two big ears!
What we've seen and been told about Betazoids is limited, but I always took the fact that Betazoid weddings involve everyone being naked points to a society where transparency was the norm. Since they're telepaths who might think nothing of hearing each others thoughts, especially among friends and family, that might have led to a society where there are no secrets or shame to hide.
One other thing that should be pointed out... how is anyone certain a telepath is not scanning people without their consent? Honestly, something as invasive as that should have some kind of blocker or 'off switch', for lack of a better word.
When you think about it, Troi's ability to sense an emotional state is impressive, given that when she's on the bridge advising Picard about the intentions of whatever alien leader they're dealing with who might be on the viewscreen, she's able to do it from a significant distance but also she's tuning out everyone else's emotions not only on the Enterprise, but also on the alien ship/planet to find the specific person speaking. Since it's implied that someone with a full Betazoid background is even more powerful with mental powers, it does sort of put things in perspective.
DS9 shows the paranoia Changelings cause within the Federation with the threat that anyone (or anything) could be a shapeshifter. It would stand to reason that a similar paranoia might have happened with the knowledge that there's a race of people who look very much like humans and they can read people's thoughts. Although, on the other hand, if you've reached the point of leading a massive interstellar government that seeks out new life, maybe a more enlightened human society sees it as just another fascinating aspect to add to the diversity of their society.