Since Aspies aren't good at "reading people," reading thoughts and feelings of people may have the exact opposite effect.
In other words, you might not even know they have Asperger's especially if they have this ability from a young age, because they can use their abilities to compensate for having Asperger's.
They might start off being straight forward about it, but, Aspies aren't stupid. If they notice that people don't like their abilities or don't like when they mention what they can see, they'll adjust, they'll just seem a bit odd.
The most powerful psychics are able to melt the brain of a single
target instantly at the range of 100 Meters.
That there is a preeettty good reason to fear anyone remotely like this. I am going to say that people will think this is a hoax or look for a more reasonable explaination. Unless there are a lot of deaths like this, in which case, yeaaah, I am kind of FOR finding your kind and making sure, at the very least, you don't breed. Because I have no idea when these powers manifest, and if a three year old throws a tantrum and heads start exploding...
So how do you escape persecution? You police your own, and track down those who have families, and monitor them, maybe training them and letting them know what to expect.
I would go ahead and lie to them and tell them that they will need a certain pill from you, otherwise there's a chance they might die so it's more likely to be reported.
Let's say I managed to warn most of my people, but sadly our powers were discovered and now governments and religious groups around the world fear us.
How, exactly? Just don't tell anyone and they never will know. But hey, that head explosion thing--I don't often stand behind religion, just going to say, it feels right, reasonable, and not at all insane to fear you.
How you do this will depend on two things: How detectable are you? and Do you have better information than the government does when it comes to tracking your kind down?
The answer to survival, whatever your answers might be, is to HIDE and find a way to track your own so that you can teach them to HIDE.
The answer to fighting back is to place people in society in order to gain information needed to keep your people hidden.
Unfortunately, "banding together" or meeting in one place in any way is likely to be a bad idea. Like the kind of bad idea that results in a building exploding. Because, you see, electronic surveillance, absent of people close to you, can get your hunters everything they need. You'd need cells, structured like any good resistance, and most of your people would not have contact with others (max 2 others, for a cell of 3).