I have my eyebrow pierced, my left eyebrow. I don't see why there might be a stigma attached to it being gay or whatever, a piercing is a piercing.
It suits me because I have quite a long thin face so it's not very noticable according to some people. Friends who had known me a while didn't even notice it straight away when I first had it done.
Generally, it's prefered that I keep it out for work. When I first got it done they told me to keep it in for at least 1 month (Cold Steel, Camden). Luckily I have had it in since I was 19 and where I work now at 25, I just take it out during the day and put it back in when I get home. I find that if i leave it 24+ hours it starts to heal up quite quick and if left much more it's a real PITA to get it back in without causing a little pain to reopen it.
If in the Police depending on how long you have had it, I suppose you could get it away with having it out for a shift and putting it back in when you have finnished.
I find the piercing ok on guys, more suited. On women it looks a lot worse, imo.