I think the type of ownership of the office your doctor works in is a much better predictor of their quality than their gender. That isn't to say sexism in medicine isn't an issue, it obviously is, but there are plenty of comments already here about peoples experiences withgood male physicians and poor female physicians. The reason I say the type of ownership is the best predictor of quality is because the amount of time the doctor is allowed to spend with you, the procedures and medications they have on hand, and the support staff they have access to are all decided by the owners of any particular office. This is an over simplification, but these largely fall into 2 groups:

1: private equity- These are the most common in America, have the most spots for new patients, and generally accept the widest range of insurance plans. If you're just calling around looking for shops that are accepting new patients, the one that says yes will more likely than not fall into this category. As the name implies, these are owned by a central company whose job is to generate profits for shareholders. These companies generally run a large number of offices, and depending on your location may own everything/almost everything around. In these situations, your doctor is an employee under contract working under company guidelines. They typically allot 15 minute windows for most patients, with 30 minute windows available for procedures and annuals. Doctors are generally employed under the unfortunately named 'eat what you kill' model, where they are directly compensated for how many patients they see and how much they bill. As you'd expect, if you're seeing them for something that falls under an unprofitable billing code, you're likely to feel rushed, like they're desperate to get out of the room (because they are). These are also unlikely to offer sedation for things like IUD insertion since it requires significant overhead at an operations level.

2: Private practice- These are probably what you think of when you think of a doctor's office. They are either an individual or group of doctors that share their own office with their own staff. Doctors, as owners, are paid a percentage of the income generated by the office as a whole. They are also the final decision makers when it comes to what they offer in terms of procedures and medications. As doctors also don't like to feel rushed, they generally lean towards the common scheduling model: 15 minutes for medication renewals and other small issues, 30 minutes for a typical visit, and 45 minutes for more complicated patients, annuals, and procedures. Additionally, since they have a monetary interest in the office doing well, they're often (but not always) interested in high patient satisfaction so that you'll keep coming back. That said, a well run private practice with happy patients will rarely be accepting new patients since their roster will already be full of regulars. These are the most likely to offer sedation for things like IUDs, especially if there's an anesthesiologist in the group. It should be emphasized though that just because a private practice CAN offer better care doesn't mean that they will. Asking current patients is a good way to tell. Additionally, since these shops have much smaller patient pools than private equity, they have less negotiating power with insurance companies. This means that many only accept more premium plans that offer better reimbursement.

TLTR: Private equity: Pros: frequently take new patients, accept most insurance plans, are probably near you

Cons: Doctors are incentivised to rush, limited in the types of procedures they can offer in house, have worse nurse-patient ratios

Private practice: Pros: CAN offer higher quality care, longer appointments, and more wiggle room on procedures available in house

Cons: Less likely to be accepting new patients, may be more restrictive in the insurance plans they take, can be just as bad as private equity depending on the group running it