Currently, pressing the comma key on your keyboard completes the tag you're writing and starts a new one, a behavior I'm familiar with by way of Tumblr but that presumably exists on other sites as well. This is all well and good if you're writing a long series of short tags, but there's another aspect of tagging that seems to have carried over from Tumblr as well - the culture of writing asides to your followers in the tags of your post.
Since these little asides don't get carried over whenever someone shares your post, they remain restricted to your followers (and anyone who looks at your specific version of a post, but that's usually just going to be your followers), and the out-of-the-way nature of the tag section of a post makes them more clearly "asides" secondary in importance to the main body.
However, the behavior described above poses an issue for these asides, in that without being able to use commas, it becomes difficult to write a sentence without it becoming an illegible run-on mess. Alternatively you could break up the sentences by hitting comma and just letting them be their own tags, but, well, then you end up with a bunch of posts tagged #but and #well.
From a technical standpoint, there also doesn't seem to be anything about commas that prevents tags containing them from working - looking at my own tags that have brute-force-added commas (either pasted on PC or added by moving the text cursor to the middle of the unfinished tag on mobile), they seem to function perfectly fine (they show up in search, they get highlighted on their tag pages, etc.)
So my idea, then, would be to create a toggle to let users disable this functionality and let them add commas to their tags by just pressing the comma key, either on the user settings page, or maybe even on the posting page itself so it could be toggled at-will. There are still ways to complete a tag that aren't tied to keys that would input valid characters for a tag, like the enter key, but I think it's also enough of an ingrained instinct from tag systems like Tumblr's that it makes sense to let people keep this behavior if they want, as well.