Is it possible to have mandibular protrusion but the teeth are normal? i.e. having a normal bite
I always think I do but I don't have an underbite (it has been fixed with braces)

Yes, it's possible. If you want surgery, you'd need to be put in braces again for however long it takes to decompensate the teeth and bring them back to their original class III position.

But my teeth are at their normal position

So you had an underbite? Cthulhu is saying if you want jaw surgery to fix your prognathism, they need to undo what the braces did then move your jaw(s) to its proper position. People's teeth can either naturally or through braces be compensated to a seemingly class I position but that doesn't correct the underlying skeletal abnormality.

Or you could have a reduction genioplasty I suppose.

No, if you had a skeletal underbite and had braces to correct it, the "normal" position for your teeth was how they were pre-braces. They will need to be brought into a class III/underbite position again before you can have orthognathic surgery.

I'm not sure if the ortho compensated but I can say that throughout treatment as my teeth got straighter, my underbite started to disappear. It completely disappeared when the ortho gave me elastics though. I think my underbite was quite a lot a dental problem as initially my lower teeth were protruding while my upper teeth was angulated inwards. I think my question is, whether it is possible for teeth to be in their correct position YET still giving me a protruding chin?

As I said already, yes, it is absolutely possible.

You can't correct a skeletal class III (underbite) with braces. You can only mask it somewhat by bringing the teeth into a class I occlusion. What your ortho has likely done is pulled your lower teeth inward and your upper teeth outwards. However, this has not changed the actual class III skeletal relationship of your jaws, only the dental relationship.

The bottom line is, if you had a class III skeletal pattern to begin with, you still have it regardless of the position your teeth are in now.

I think you're not getting me. I am saying the teeth are in their normal position, and the ortho did not compensate to mask the occulsion.

If you had an underbite before your braces, how could they be in their natural position now? Your natural position was an underbite and braces "corrected" it. Get it? Just because your teeth look fine now and you have no functional issues, doesn't mean your genuine class I. If your bite is acceptable to you now then as I suggested, look in to having a genioplasty.

No, as in they are straightened but not compensated i.e. not tilted out of their ideal positions to mask the underbite

So let me get this straight: You had an underbite, but they didn't have to change the position of your teeth in order to correct it?

OK.

There are 2 factors that may contribute to an underbite: teeth angulation or jaw discrepancy
If your lower teeth is tilted outwards and upper teeth inwards, you would imagine the person would have a pseudo class III malocclusion but not really when you straighten their teeth back to their normal position i.e. not tilted but STAIGHT.

If another patient has a jaw discrepancy issue, the ortho can choose to tilt their upper teeth outwards i.e. past their 'straight' position and lower teeth inwards (again out of the straight position) in order to mask the underbite, this obviously does not fix the jaw issue.

So if you believe the maloclussion was purely as a result of "teeth angulation" rather than a jaw discepancy, why do you think you might need orthognathic surgery? You're either a skeletal class III or you aren't.