A question on the use of brackets. [Details inside].

It is a bit awkward to have the start of your sentence be parenthetical, partly for the reason you describe. Usually a sentence should stand alone without the part in parentheses, so you capitalize the un-parenthetical part as if the parenthetical part did not exist, and then you capitalize the parenthetical part as if you were adding it to the parenthetical part, but in this case, if you do that, you end up with an odd capital in the un-parenthetical part, which I think is most correct if you do write that, but if you were concerned with best formal writing practices, I would recommend not writing it that way.

If you do write the words you used, I would put the parentheses like this:
“You (have the feeling that you) are being followed. What do you do?” and I would leave out the ”(men and women)” part, since that includes everyone, and since you explain in detail in the following description.

Assuming you did need the ”(men and women)” part, I might write:
“You (have the feeling that you) are being followed. What do you (men and women) do?” Having ”(men and women)” where you did in the sentence, I would call a fragment (i.e. not strictly correct).

I might also avoid parentheses entirely by writing something like:
“You think you are being followed. What do you do?”

(Those ( ) are parentheses. These: [ ] are brackets.)

I think of anything in (parenthesis) or [brackets] as a start of a new sentence so I just capitalize the first word. Just like in math, items in (parenthesis) or [brackets] are it’s own thing for the most part.

I don’t know for sure, but here’s my intuition:
If it were a “real” sentence—(You have the feeling that) you are being followed. I would think it would follow rules similar to a semicolon, where technically two sentences could stand alone, but they’re joined; capitals mark the beginnings of sentences (and proper nouns,) not any phrase that could be a sentence on its own. So, in this case, even though “you are being followed” could technically be it’s own sentence, and essentially is, it’s still not beginning the sentence, and so, its “you” is not captilized.

As a question-title like you have, I think either would work, though. Also, they both feel a little different, at least to me—
(You have the feeling that) you are being followed.
(You have the feeling that) You are being followed.
When the second ‘you’ is capitalized, it makes that part of the title stand out more, become that much more important. Like, the feeling is really strong, so strong that the fact that it’s an un“proved” feeling is a just a parenthetical before the point, and really NOT the point.
When the second ‘you’ is lowercased, the assertion/claim that ‘you’re being followed’ is a continuation of the feeling—out in the un-parenthesized world as well, but more attached to the fact that it’s ‘just’ feeling.
(I hope I was able to make that make sense.)

Your sentence should be capitalized as:

(You have the feeling that) you are being followed; (men and women) what do you do?

However, I wonder why you need so much information in parentheses? Couldn’t you simply have said:

You have the feeling that you are being followed; men and women, what do you do?

I think by putting the first part in parentheses, you are saying:

You are being followed, though there’s a chance it may all be in your head.

Unless that is what you mean, I would leave out the parentheses entirely. As to the (men and women) bit, I can’t think of any reason why you would put that in parentheses. So again, I would leave them out.

I understood all of your answers, it gives me possibilties for future use.
Thank you alll!
@dappled_leaves Yes, that is actually precisely what I meant it to mean: you are not sure you are being followed, however, you think you are.

@rebbel; How about this?

You are not sure you are being followed; however, you think might be.