it's a PGA tour event. I am not sure that there is provisions in the PGA charter that says you have to be a man to compete in tour events.
It's an invitational event, not an open event. She received one of the 8 sponsor's invitations. The players taking exception to the invitation's main objections is that she is taking the place of a PGA Tour player. They think if she is to play in a PGA event, she should qualify for the Tour itself, not just get a Sponsor's invite. The Tour players are also miffed when those invites go to other non-Tour players in a PGA event, so this is not the first, nor will it be the last time, that PGA Tour players squeak and moan about Sponsor invitations. The only reason it's getting any publicity at all is that the invitee in question lacks a noodle.
They make a legit argument. Also, Singh's comments were mostly taken out of context by the reporter, and even the words were manipulated according to an article I read today.
What would be interesting, is if she tried to qualify for an open event without getting a free ticket into the event. Then anyone squeaking about it would have absolutely no ground to stand on. She would have earned her way into the event, instead of getting a backdoor Sponsor's invitation.