Let’s get one thing straight. The police are here to protect society, to enforce the law. I know better than most that not every cop is a hero (I was once beaten by copy due to mistaken identity), but most cops are good people just trying to help us, the civilians. To be offended because a woman who has put her life on the line to protect society is touching you, is bigotted and foolish. Would you be offended if a female firefighter or soldier saved your life or carried you out of a burning building? Would you be offended if you collapsed on the street and a female EMT revived you?
For what it’s worth, the gabbay/driver of a gadol told me that when his Rav used to fly at the end of his life, he was often assisted by female flight attendants. He never once asked for a male to help him, and was very polite to the flight attendants and appreciative of their assistance. I asked the gabbay how this was OK, and he said that the Rav said that this wasn’t derech chibbah. It’s like a nurse helping you.
There is nothing wrong with a policewoman enforcing the law. If you are concerned for hallachik reasons about negiah from a policewoman, don’t break the law. If you believe that you are entitled to protest a law, you must be willing to accept the consequences. Speak to your rav and make the right hallachik decision.
BTW – I asked the shayla about going to female health professionals, and there are different shittos. It’s not black and white, and I’m not sure this is the same thing. I can choose my health professional much of the time. I cannot choose which police officers are on hand.