Interesting idea. I can only say if someone is so petty as to not show again after getting a low numbered tag, you are well rid of them.
Chess Club Membership Tags. Has any other club done this and has some pointers?

Honestly, having played both golf and disc golf at courses where members have bag tags, I've never heard of competition for lower-numbered tags. I mean, it makes sense and sounds fun, but in my very limited experience one's tag number was one's club membership number so swapping tags would get really confusing really quickly. In your concepts, is that the case? That the tag number would be the membership number, or would they be unrelated?
My suggestion would be either a blind drawing or simply starting the numbers you give out at a high number (like one did with new checks back in the day when retailers would be leery of low-numbered checks), and/or making sure to draw new numbers with each year's membership. That said, I can't really tell from your post if you want to discourage or encourage the tag-swapping, or if it's still an open question for you, too.

Something like this is what I talk about. Not a membership number, sort of just a numbered tag, usually has a year (So they get refreshed every year and users will need to be up to date on their membership.) https://www.pdga.com/news/tag-em-bag-tags-add-competition-club-play
I'm thinking we're going to implement something like this in our club. I agree, about who cares if someone takes a low numbered tag and doesn't show up, it won't be missing for more than a year. But we can deal with it later if it becomes a huge problem. I'm trying to source a company that will make metal or plastic tags/keychain type tag etc at a reasonable price.

They came in yesterday, and they look great. We're going to be giving them to our members starting next week. I got 1 - 40, we're not 100% sure what our tag game rules will be, but there will be tag games/matches for which you put up your tag, and the winner of the match gets the lower number. Similar to the other sports.
Hello CB&E, got a question. I'm in a fledgling chess club in the deep south, and we're working on some ways to promote and give us comradery as a club. So I was exploring the option of maybe printing some club 'bag tags'
Let me explain. I've played some disc golf in the past, and it's quite common for disc golf clubs to have yearly 'bag tag' challenges. These are metal or plastic, or leather or wood, etc. tags that typically hang off your disc golf bag. They usually have a year, and a number 1-XXX (Whatever, depends on club size)
Having the tag, essentially means you've paid your dues for the year. Also, it gives a fun little game in that if you're out and about and see others, with a tag, you can play for tags. In which both players throw their tags up on the chopping block, and the lower score of the round gets the lower numbered tag (Almost a ranking as it were). There are sometimes also club minis, in which large groups will get together, and all throw their tags in, and then among the players tags are divvied out to everyone back based on where they finished in the group.
So converting that to chess has some challenges. Our club meets weekly, for sure, and we have little blitz tournaments that we could use for the large group style tag challenges. But saying I'll play you for tags has problems in that you've got the inherent, black vs white pieces, so it's a little different. etc.
Any thoughts? I never cared about the number of tag I had throughout the year, but it was always fun to try to get a lower numbered tag.
There's also some issues with people getting high tags, 1-10 and then never showing up again because they don't want to lose their tag. I could see some people getting upset about that, but wanted to see what other individuals who know chess think of the possibilites behind that?