Product Taxonomies, on the whole, are iterative in nature. If your company starts selling products it's never sold before, you might need to add new taxonomy. Are customers or site metrics saying your navigation is bad? New taxonomy. 10,000 products in one miscellaneous category? More new taxonomy!
An agile methodology seems at first to fit in nicely. After all, you're maintaining these categories in a very dynamic environment where priorities might shift, actual changes are being made all the time and the cost of rework can be high. There is a lot of collaboration among product managers, product data teams, merchandisers, IT, management and more. According to the tenants of Agile, it's a perfect match.
Except it's not. In Agile, each iteration (or sprint) is empirical and followed by feedback from the business. In other words, you may deliver changes to a product category that may be followed by suggestions to make additional changes to that same category in the next sprint. In the world of taxonomy maintenance, incorporating this feedback won't reduce the cost of rework because the downstream effects of those changes remain the same. More products will need to be categorized or re-categorized. Those products will then need to be tagged and their attributed data populated. The changes made during each iteration are defined and need to be repeated each time, which relates much more closely to traditional project management principals than Agile. Also, because taxonomy maintenance is ongoing the lowest priority tasks won't be removed from the project altogether and will instead be scheduled for a later date. After a short while, you may find your project teams are running traditional increments that just keep growing in scope rather than actual agile iterations.
Your teams can borrow elements from Agile without having to upend the way projects are managed now. For example, holding cross-team meetings to present taxonomy changes is a great practice, but force-fitting an Agile methodology where it doesn't belong may cause more harm than good.