(I work in an urban hospital)
It's a give and take.
I'm a big dude and I look like a bouncer at a biker bar. I work in an ICU and I get the lion's share of the requests to help pull patients up/ turn patients or move them to bedside chair/commode. Also, they usually give me all the sexist male, uncooperative or combative patients.
I never bathe a female without another female in the room. I never do gyno exams and I've never put a foley in a female. (I'm actually proud of that last one...what a streak). When cleaning up after a BM, I always have my fellow female nurse clean the vaginal area.
I will help a female pt to the toilet and stay in the room for high fall risk, adjust/apply cardiac leads, help on and off bedpan, dc a foley ...(anything without any direct vaginal contact).
All the female nurses on my unit know that there is a standing offer from me for care of their male patients in the same way that I ask them to care for my female patients.
Luckily for me, most a/ox3 females prefer a female nurse to perform my "hands off" list above. However, even if the patient had a 21st century view on male nurses I probably wouldn't anyway. Why open myself to potential accusations? I have too much to lose and it isn't worth it to me.