Male or female, I would also have been uncomfortable with a circulator who did not establish some base level of rapport, check my wrist band, and ask me all the questions that have already been asked 3 times by everyone else. There is more to being a circulator than showing up and wheeling the patient back, and charting and running for supplies. We are still responsible for our own pre-op checks, which includes talking to the patient, asking questions, going over any concerns BEFORE SEDATION HAPPENS. It sounds like this nurse did not do those things.
It's not about the male being a NURSE. Note how the OP stated the other two professionals INTRODUCED THEMSELVES. The nurse failed to act professionally by establishing rapport and doing a thorough intake during a sensitive time, and that is the problem.
Now onto the gender thing and the trauma response, since some of ya'll don't seem be able to put 2 and 2 together here:
Given the sensitive nature of GYN procedures and the FACT that 1 in 6 women are survivors of sexual violence ( which is largely perpetrated by men... cue the #notallmen response, or better yet, spare me...), and likely have some level of PTSD around that, it is understandable that in a vulnerable situation, especially where the RN failed to establish trust and rapport, that the patient's amygdala would take over.
As nurses we should know that the sympathetic nervous system response can hijack our rational brains. Yes a patient can logically "know" that nurses are professionals, regardless of gender. Yet their nervous system will still scream "UNSAFE!" at them, which is why our JOBS as NURSES include establishing trust and rapport whenever possible, to the best of our ability, regardless of genders involved.
Most people have had some level of trauma in their lives. Surgery is a time when folks are already nervous, so these buttons can be pushed more easily, and an experienced circulating RN should know that and try to reassure the patient. The least we can do as circulators is make some eye contact, make some conversation, and put our patients at ease. This nurse, whatever their gender, FAILED to do that and the patient felt unsafe, full-stop. OP, you have every right to feel as you did. Don't let fragile egos of the #NotAllMen crowd make you feel otherwise.
If the circulator did not even do the basic pre-op interview and couldn't be bothered to introduce himself, as a patient I would be wondering what else that RN is not good at. Surgical site cleansing? Sterile field monitoring? Yes nurses are "all professionals" hopefully, but we still need to reassure nervous patients by actually presenting ourselves as professionals. This includes introducing yourself instead of hovering awkwardly. It includes asking pre-op questions even though the admitting nurse has already asked the same questions. It includes asking the patient if they have any concerns before sedation starts. This nurse did not act professionally, so the patient should not be expected to trust blindly.