A few things.

Firstly, OP specifically said "Ideally without disclosing I'm trans". Your whole comment was unnecessary first off from the outset.

Secondly, you have grossly overstated medical necessity here. Hormonally trans women who have been on HRT are functionally much closer to cis women than cis men. Trans status is rarely relevant to any medical treatment that isn't specifically about reproductive organs.

Thirdly, trans status is a matter of life or death in the vast majority of the world. Medical necessity, even if it were as significant as you've tried to portray it as, means nothing if you get arrested or killed.

The moment I told my psychiatrist I am trans I was denied further care. Your advice is wrong and dangerous. See Ada's comment for more detail on why.

Edit: For more context I live in Norway where this is highly illegal. I've complained to both the hospital and to higher authorities, but to no ones surprise there's no response yet :)

While its true that there can be implications for the efficacy and side effects of medication if you're doing hrt. You can also check for those interactions before you get your prescription or ask someone who you know to be safe. It's going to potentially be safer than being denied care all together. a lot of places are extremely transphobic if not in policy then in the personal prejudice of people generally.

I may be wading into a minefield here

You are. And not only that, you're in a community aimed at trans folk, offering advice to trans folk who are aware of the reality of the situation in a way you very likely are not. That's not a good position to start from when it comes to offering advice. Doubly so, when your advice appears to be coming from a position of "in a perfect world" rather than from the practical realities that trans folk have to deal with in the world as it is.

I've learned it's actually pretty important for doctors to know someone's status as trans

As with all things, this depends on the context. Sometimes, it's relevant. Mostly, it's irrelevant. And sometimes, knowing causes doctors to make mistakes about our healthcare needs when they incorrectly assume our medical symptoms align with those of cis folk of our assigned genders (this is particularly likely if the doctor is not familiar with trans health care).

On top of that, there is a thing called "trans broken arm syndrome", in which doctors tend to immediately aim for HRT or transition surgeries as the cause of whatever ailment the trans person has. Again, this is particularly true with doctors that don't often treat trans patients, or worse, that hold anti trans opinions (even if they keep those opinions private).

Yet, even when it is relevant, telling the doctor can lead to all sorts of othering and exclusion. Sometimes, it's outright transphobia and misgendering. Sometimes, it's being isolated from other patients, because the medical staff don't know how to deal with you. Sometimes, it's just medical curiosity, where the doctor just wants to ask all sorts of irrelevant questions out of medical/personal curiosity, because they don't often deal with trans patients.

I live in a very trans inclusive country, with protective laws. I'm openly trans, and wear a trans flag dog tag, and a trans flag arm band. Yet one of the few situations where I won't openly out myself unless I have no other choice, is when dealing with medical staff who don't recognise those flags. And I do that, because the folk who don't recognise the flags are the folk more likely to other me, more likely to be confused by me, and more likely to ensure that my interaction with them is as uncomfortable as possible. And that's in a safe, accepting country. Imagine what it's like for folk who live in places where transphobia is not only common, but sometimes legally mandated...

Which is to say, each and every trans person navigating healthcare has to decide for themselves how to walk this tightrope. And general advice of "you should tell them" suggests you're not familiar with the lived realities of trans folk, despite working in a hospital

The medical system lost its privilege to know everything about me at all times long ago. It's positively lousy with conservative quacks, who not only lose all sense of professionalism when it comes to gender minorities but downplay cis womens' medical issues too.

What are some examples of the biological implications and risk factors? As far as I can tell the only one I can think of (and the only one my doctors told me to disclose) is that I have a prostate, but risks of prostate cancer are very low when estrogen dominant.

Either way, assigned sex is often arbitrary and a can be a poor indicator of the medical situation, e.g. 20% of intersex individuals are trans and may or may not have typical anatomy of their assigned sex. So communicating you're a trans woman gets misunderstood as "I'm male", which is not the correct conclusion.

I should also state I obviously disclose my trans status to doctors who are providing care like HRT, or who need to know for other reasons (e.g. a gyno who would perform a prostate exam through the vaginal canal).

But my question is for contexts where it's not appropriate or necessary to disclose trans status, such as walk-in clinics or ER visits.

I assume you are cis from your comment, but you should know it's not just the prejudice and mistreatment that motivates not disclosing trans status (whether overt bigotry, or other forms of discrimination like "trans broken arm syndrome"). When you tell someone you are trans, it immediately undoes your gender in their eyes. It can feel dehumanizing, and it also comes with a lot of bad assumptions (e.g. that biologically I'm not different from other men, but also that I must be like a man in other ways, too).

For that reason I find it's actually better to just disclose necessary information without framing it as being transgender - I disclosed that I was born without a uterus, and I disclosed the hormones I take and in what amounts, etc. which is what they need to know.

EDIT: I should mention, I've responded to a similar comment in the past, I'll throw that inline here for convenience:

EDIT2: another way trans status might impact health is for directing them for certain kinds of care that impact the community, such as testing for HIV, connecting with drug abuse resources, etc. - but that's rather generic and less of the kind of "biological implications" you mentioned, but it's an angle I hadn't thought of before (if we were thinking about policy choices this would be something to consider, but in terms of what I as a trans woman should do, it feels less relevant).

For an ongoing relationship with a primary care doctor or a specialist for a new health problem that my GP has referred me out for, sure. For something like the dentist or an urgent care doctor because I have an ear infection? Absolutely not, I’m not trying to deal with trans broken arm syndrome.

If I have concerns about medication interactions I’ll ask the pharmacist at my local LGBT health center. The odds of there being a medication only cis men can take (for reasons other than fetal health) or that the dosage is going to be drastically different because of my sex rather than my hormonal profile, medications, and weight is vanishingly small.

Assuming you're not a trans woman, nobody asked you. Maybe don't go blundering into minefields.

Finding new doctor is the worse experience every.

Here in public health your town gets a few of them, and you can only change between those.

The procedure takes days, more days to take new appointments and then to suffer the issues again.

That is really shit. You get no spoons to even start again.

aw, I didn't get to see what you wrote :-(