Vlad,
At the same time I do not want to allow the business that is meant to serve users globally be led by mine or any employee's personal emotions and biases and this is why for Kagi we have principles of operation.
You are already interfering with the small web initiative (as you've said prior). I personally love this for my own search results, but it does skew towards content where the authors have the technical means and conviction to sideline the typical writing tools people use for either ease of accessibility or reach (e.g. Medium, Substack). To be blunt, you built a technocracy web initiative.
Evidence or research that suicide hotline widgets actually help in meaningful way.
That's a very utilitarian view. Morally, you may just not want to be involved in facilitating suicide. It was irritating when we exchanged emails and it is irritating to me now that you do not seem to grasp the difference between suicide and assisted dying. They have vastly different motivations and suicide, being the much more common, is usually linked to an acute state of crisis. Even though I'd generally be in favor of assisted suicide being available, there's still an ongoing discussion about the possibility of induced demand for such in Canada. Neutrality is not a neutral moral stance.
How do you deem one set of those morally acceptable to be left out unattended and intervene with others? This is the slippery slope question.
I think this is the hardest question in the room, but the absence of absolute answers does not mean you can avoid the question. Saying the line is fuzzy and concluding the line ends right below the wall of one side of the room because you are uncomfortable by the existence of the problem are entirely different things. I don't think you can claim to "humanize the web" and not answer this question for yourself and for your users when you act like every other large corporation and do the legal minimum.
Frankly, I personally don't consider interference with any of these queries a problem as long as it's reasonably established that's actually what someone is searching for (including intent, which is hard, and why most of these wouldn't work) and you are transparent about the request having restricted or specially curated results, because lack of disclosure (as common pretty much everywhere else; even up to using such info for marketing) is much more dangerous. I also think places like that suicide cult forum (from the article I sent you) or Josh's doxing and bullying forum should indeed be removed from the index, with a note that unsuitable results have been removed (similar to Google's DMCA removal notice).