beta
There's nothing in the raws that indicate whether the doctor is male/female/other. The way they speak is very gender neutral, as to their name. This doesn't mean they are automatically nb or trans etc.; we simply don't know yet. it's completely natural for them to speak this way, especially given their distant personality and minus the occasional cuss word (which I saw like once), it's just professional.
However, in ch 9 Shizuma says "this is the men's [changing room]" which implies he thinks the doctor is a woman. Their response however was just "huh? yeah..." which doesn't give us any further clarification because it could be they were fully aware and there's nothing wrong with them going in, or they didn't know before but it doesn't affect them very much (the doctor isn't very expressive afterall).
This is just my own speculation but I think the story will go in the the "oh no, shizuma is getting close to a beautiful woman and since he's straight he's going to fall in love. plot twist that beautiful woman is actually a man so you have nothing to worry about, minato!" direction because of that scene that specifically shows shizuma thinks dr.onodera is a woman, and the last page of ch 11 where minato is very shocked (although he could be shocked for other reasons such as the possibility he knows dr.onodera).
Overall i think the safest way to refer to the doctor is using they/them until we are given more information because it's gender neutral; however since it isn't confirmed please don't fight with other people in the comments if they use he/him or she/her. there are no "correct" pronouns because nothing is confirmed so any pronoun is a valid theory.
Edit: someone reminded me that in the first chapter it is mentioned that the clinic was run by all-women staff so it is more likely the doctor is a woman.