In the TNG episode Tin Man we see a Betazoid (Tam Elbrum) who was "woke" to his telepathy at birth. As such, we see that, even though he is considerably gifted as a telepath, he also doesn't have an actual filter. What's odd is that he casually reads minds in ways that we see other Betazoids get negative reactions to, and yet nothing is ever said or done about it.
TROI: Well, in most Betazoids our telepathic gifts develop at adolescence.
PICARD: You mean you're not born reading minds?
TROI: No. Except for some reason that no one understands, occasionally a Betazoid child is born different.
PICARD: How different?
CRUSHER: Born with his telepathic abilities switched on.
TROI: Most Betazoids born like that never lead a normal life.
CRUSHER: The noise of other people's thoughts and feelings must be overwhelming, incomprehensible, especially to a child.
TROI: And painful. Early diagnosis and special training did help Tam adjust, but he has some problems.
And later (emphasis mine)
TAM: How're things in the land of the living?
TROI: I thought you might be lonely. No one sees you except Data.
TAM: Lonely? I can hear everything that everyone on this ship thinks. No one besides you seems to be missing my charming
TROI: You want them to dislike you. Why?
TAM: Because I'm not a nice man. Okay, okay. Because they scare me. They're too many minds. I can't shut them out. I never could learn. All their loves, their hates, their fears, their needs. It's like a tide that never ebbs. I could drown.
When the Enterprise is attacked by Romulans trying to reach Tin Man first, Tam reads the mind of the commander of that ship and knows their full plan, and thus he gets Tin Man to attack the Romulan ship and destroy it (damaging the Enterprise in the process).
Tam represents the only Star Trek telepath that could casually invade minds like this and not at least have people "creep out". Whether this was due to his being born this way or being a valuable Starfleet resource is unclear.