Would it be inappropriate to cite wikipedia for something trivial in an academic article?

The real question is whether you should cite anything at all. You're not writing an article on golf clubs. You're writing an article on statistics.

Is your example so complex that you need explanations upon explanations about why you're choosing this parameter, and that, etc, and if a reader doesn't know all this then the example is not understandable? It it really that important? Then you're wasting your reader's time with a digression that's largely irrelevant to your scientific work.

Is the example sufficiently simple that to understand it, very vaguely knowing how golf works is sufficient? Then why would you want to cite anything? I don't need a scholarly article to explain that if I were to choose a golf club, I need to consider its length, its weight and so on. It's pretty much common sense. Do I know more than that? No. Do I care? No. Is a statistics article the place to learn about such things? No.

Yes, you should look at the golf literature itself. It is relatively accessible (not like drug design). You can find good review articles on club construction and selection.

Because you are mostly looking for an example for your method (versus really analyzing the golf clubs), I think it's fine to just pick one decent golf club review article (even a popular one, or from a manufacturer) and use it, versus totally analyzing the literature. For example if one article has 6 attributes and another has 7, just use whichever you choose. Also, of course, make it clear in your own text that you are just doing an illustrative example, not writing a definitive article on club selection (e.g. a caveat that some other articles use different number of attributes).

Statisticians should have the ability and the proclivity of skimming literature from many other fields. You don't need to become an expert. But you do need to have some level of outreach. Consider if instead this was oil exploration or drug design (more momentous business decisions). Note that this habit of dipping into the literature of other fields, not only keeps you grounded on those fields but will tend to give you ideas and insights for applications of statistical methods.

If you stick with Wikipedia, you are relying on user content, that is not well archived. In addition, the cite will be distracting to your readers and reduce trust. Since it's just an illustrative example (you could pick anything), there's no big need/plus for introducing a Wikipedia citation.

If you show too much the attitude of "who care's, it's a silly example", it will distract the reader. This is not just an issue of the Wiki cite, but your general approach on the illustrative example. And no, I'm not expecting a master's thesis of research on the example problem. But still be thoughtful about the problem selected (field, clarity, references, etc.). If you are not, it will be distracting to the reader and reduce trust/interest in reading the details of your method or thinking about how it (or you) can be useful in applied settings.

No, its not inappropriate, but is a bit dangerous since wikipedia is a moving target. Things there change, though for your example, probably not enough to be a large concern. But you should, at least, give the date of access as well as the link to the article (or the paragraph within the article).

Note also that over time, things can change a lot. Articles printed on paper in journals distributed via sneaker-net have a long lifetime. Centuries, perhaps. Will wikipedia still exist when you are ready to retire in 30 years (say)? Perhaps it will. But a lot of online social media sites have simply disappeared in the past 10 or so years.

That isn't necessarily a reason not to use such resources, but you should be aware that the world as it looks today will change a lot over your professional lifetime, so be prepared to speak to future readers, not just the current ones. Make it universal and eternal if you can manage it. Exceptions, of course, if you are explicitly discussing current forms of media.