Dido Grigorov: Categories - yes, it is better to be indexed :) all products too, but tags - no :) but you can use them for internal link structure and better relevancy ;)
Rob Woods: if it`s product category pages I`d say "usually" index them, if it`s product tags, "usually" not, but both depend on what your searchers want, how unique those pages are from each other, and the value of the content you provide on those pages
Dido Grigorov: Yes :) absolutely :) If you can provide original, unique and useful content for all types of taxonomies - then go ahead and index them, but be careful with the amount of duplicate content!
Cody Sharp: If you can add content to the tags and category pages, then yes. I use the Avada theme which now allows for you to build out content using their normal editor on woocommerce tags and categories.
Dawn Anderson: Depends on the value added by the categories and tags. Folksonomy can be a place where copywriters / content marketers go a bit nuts and just create tags with every possible word that pops into their heads (including their own name I`ve seen). They succeed in creating a tag cloud which messes up the topic theming of their own site I`ve seen before now. By the same token I do use some tag when I don`t believe there is enough justification for an individual category for more nuance but it has to be relevant, very relevant. Avoid thin and too many of them and just trying to spin the same few posts into as many places as possible.