No. No one has said that women should not request female care providers if they want to.
A few people have said they don't feel that way, or they don't personally identify with that feeling, or find it weird. Some have said having a non-prefered sex carer would be better than no carer.
But no one has said that it shouldn't happen. And as far as it goes, it's normal practice when its at all possible.
The woman in the original article ran into trouble because she had specific needs, and was at a very small hospital with only one or two doctors, and had not bothered to make any contact ahead of time to make sure they could accommodate her.
One of the reasons to do prenatal care is not just for the checks themselves, but to meet the doctors and midwives and have your needs assessed. One thing that might come up is that a particular hospital has limited staff, and maybe a different one would be a better choice for a mother with specific needs.