Is a letter of recommendation from a suicide line worth anything in academic career in STEM?

If you have a PhD, a letter that does not describe your teaching and research ability is not helpful for applying for academic jobs.

So no.

If you have to write a diversity statement or some other such non-academic statement, then you might want to mention this experience in it, but I would advise against including an actual letter from where you worked, as this will likely seem a bit strange and probably also goes beyond the intended application materials you are requested to submit. Moreover, even if you have to write such a statement, I think mentioning this experience would be more appropriate when the position involves some teaching. In any event, if you're not sure, then I would go with what @Anonymous Physicist said and not mention it.

Incidentally, certain subfields of psychology are considered STEM, I think, and probably for psychology such a letter would seem a lot less strange and perhaps even helpful. Indeed, in some research areas not restricted to STEM (e.g. suicide prevention research), such a letter would be very appropriate.