To answer your title question is complex.
Sensitives are culturally outcast, and have been for a long time. They have always existed but in only a few cultures have they been accepted, and occasionally, revered for their abilities. Most of the time, they were pushed aside, ostracized..., or worse.
A lot of this has to do with Judeo-Christian belief, particularly that rooted in demonic works. To see spirits has been considered the work of the devil in the Christian world. We are still heavily influenced by medieval attitudes in the modern world, whether we know it or not. Plain and simple, ghosts are to be feared and those who see them are in league with evil.
Even in non-Judeo-Christian cultures, the ability to see spirits places the sensitive outside the realm of what "other" people can do. Like being red-headed, or crippled, it makes you different. And difference is the root of all prejudice.
Truth be told, today is probably the best time to be a sensitive. With the backing if the scientific community and even much of the clergy, knowledge of the paranormal universe has been accepted widely. Even the ardent skeptic admits to the existence of the paranormal - by his own denial.
For the rest of humanity caught in the middle, they may not admit to that which they cannot see... but they are willing to concede it is possible.
That is a big step forward.