In EQ, the ability to 'inspect' people was annoying enough to some that eventually Sony added the capability to prevent someone from doing it, if one so wished.
When someone examines me without asking first, I feel a bit violated. Perhaps that is because I am female. Logically, I know it is not a 'sexual' thing to have one's armour examined, but, emotionally, I think it is an ingrained reaction to what can feel like being 'touched' without permission. All anyone has to do though is ask me nicely first, and of course I will say 'sure, go ahead'.
However, even if people don't ask, if they only do it once and move on, I try to ignore it without comment. I am not sure if it is possible to inspect by accident in FFXI, but, it was in EQ (unless/until set to 'no inspect'), so I do have some tolerance for 'mistakes'. If they stand there and repeatedly do it though, I regard it as childish and annoying at the very least.
In my case, I have never, in any game, ever had any armour that really was worth gawking at .. so I think most who do examine my person are either doing it out of pity (some try to hand me equipment after seeing how poorly dressed I am LOL - and nope, I won't take it), or because they have not grown up yet and can't resist any temptation to see what they can get away with or get a rise out of someone, or just because they know it will annoy me.