Is there a small part of the population that is against it? Sure, and there probably always will be. There is also a small population of xenophobes and racists, but they definitely aren't the majority.
I've actually heard quite a few women opine that they start out suspicious of women in powerful positions these days, because they know directly how easy it is to get there on the back of feminism, but they need competent services in that moment and not a job.
Just to fill you in, people are suspicious of people in powerful positions. Right now, folks that agree with you blame feminism. Previously, they'd say it was obvious that she sexed her way to the top. I'd not take any of this seriously.