Short story - unless you are okay with an overly long interview process and having your current manager know you're looking for another job, don't waste your time applying for this job.
Long story - The interview process started off good. I had applied both to the IRB/APLAC Quality Improvement Manager and the IRB Manager positions, but was initially interviewed for the IRB/APLAC Quality Improvement Manager position (phone interview and first Zoom interview). After the first interview, I had a second interview in which I had to give a 5-10 minute presentation on an IRB-related topic. Although the interviewers liked the presentation, they had me interview for the IRB Manager position a few days later. Okay, that's fine, but then I had to also complete a written prompt on IRB topics within a certain time frame after this third interview. They then had me interview with another higher-up in the department (now on the fourth interview, although it still had not been made clear which position I was even still being considered for). The higher-up informed me that the group had positive feedback for me so far and that the hiring manager for the IRB Manager position would be reaching out to me soon.
A couple of days later, the hiring manager sent me an email requesting me to call her. She requested over the phone that I provide her with the contact info of my current direct supervisor as a reference. I told her that I did not want to do this as this would put me in a bad position with my current employer as they did not know that I was looking for another job. I even emailed this hiring manager back the policy publicly available on Stanford's website that said that job candidates could provide former supervisors as references in lieu of current supervisors. However, she requested that I call her back, and told me the same thing.
I thought it was strange that, not only was she requesting this info, but also that she would not put her request in writing to me (only requested during phone call) and still pushed for it even after I pointed out the policy. I ended up sending an email to her and several others I interviewed with during this long, drawn out interview process that the request was unacceptable and did not align with their publicly available policy. I said if my alternative references could not be considered, then they would need to withdraw me. Their response was that they would "discuss further with Stanford." That was several months ago (this was back in May/June). And guess what? Both positions are still on their website, probably because no sane currently-employed job candidate is gonna ask their current boss for a reference if they're keeping their job search a secret.
After completing 5 interviews, a presentation, and a timed written prompt, it definitely was a waste of time and effort for an individual contributor role. Based on the current direct supervisor reference request alone, I would not consider applying for a job here again.