@carstenfranke So when it comes to pronouns, there are many factors to consider. Keeping in mind I myself am trans, I will walk you through what that "point of decision" looks like from my perspective.
When I encounter a pronoun field on an online form, the first thing I look for is a "required" indicator. If the field is not required, most non-transgender people will skip it, or they'll write something incorrect/slightly off-base, like "male/female" or "normal". If I write anything in that field, I am potentially outing myself. I will usually avoid the field, *unless* it is a situation where I know everyone involved, it's a transgender-specific space, or the alternative (being misgendered) would be worse. For me, one of those "alternative is worse" situations is a doctor's office.
If it's a drop-down, I will check the options available - this will give me a good idea of the intent of the form writer. If the options are he, she, or "other," this tells me the person making the form doesn't know about nonbinary people, or doesn't care. They might be okay with me as a "binary" trans man, but most non-transgender people don't see the difference between us, so it's still not a good idea. Avoid again. If they have a LOT of options, even ones I've never heard of, I might put it down - but if it's optional, again, I'm more likely to skip it, even though a field like that is ostensibly made for people like me.
If the field is required, I will put the best available option that does not make me look suspicious, because I know cisgender people will also have to fill it out. Some trans people don't want to "pass," but I am someone who does, and that is my goal personally in these scenarios, to either be perceived as my true gender or to fly totally under the radar.
However.... As discussed in the post, for cybersecurity reasons, it may be better to not collect this information digitally.
Paper/sticker name tags at an in-person event would be a good alternative, if your club meets in person, yes. But in that situation, you will still have the problem where non-transgender people skip that step, and in doing so, inadvertently out the trans people in the room.
If you can, I might recommend a name tag sticker template that includes a pronoun field. That way, when people fill out their name tags, they will be reminded to list their pronouns. Some may still skip it, but some will do it. Also, modeling is important: group leaders, especially cisgender leaders, modeling "pronouns on nametags" goes a very long way.
However, if you know there is a trans person in your group and **if they have disclosed that to you,** consider asking them if they have a preference. My general advice is, yes, I think you are right to reconsider the field on the online form, this is a very difficult decision to make but it's probably more risk than it's worth. But if those within the group have opinions, their insight may be more valuable than mine as an outsider.
Sorry for the long response, feel free to add anything else or ask more questions. This is a good one!