When my mother went into care, she was asked on day one, as she was admitted, lots of questions about her likes and dislikes, and one was about her preference for female or male carers and intimate care. She specified only female carers for intimate care, but was of course happy for any other cate to be either sex. In fact, one of her favourite carers was a man. This is how it should be. Although she was self funding and therefore paying a lot of money for her care, I think that all residents should be afforded the same consideration.
When she had carers at home, I wanted her to have female carers, which was what she requested anyway, because whilst rare, I was aware that as an elderly lady living alone, she was vulnerable, and whichever way we want to look at it, men assault women a lot more often than the opposite. I felt she was safer with female carers when she lived at home.