Does any built-in Lightroom gallery or some third-party gallery support Lightroom’s tags? It would offer more navigation possibilities for those looking at my galleries. I am running Lightroom 6.
If you mean online gallery, certainly not Adobe's Revel. IIRC it doesn't even SHOW exif keywords.
Flickr does a decent job with keywords. It shows them, and clicking one as a button takes you to not only all your photos with that keyword, but everyone else's, in two separate groups (perhaps there's a way to limit the filter to only your own photos).