Micha
Unless you have 100,000 or more URLs on the site, you can't "save crawl budget" by any trick in the book.
And "noindexing" pages doesn't prevent search engines from crawling them. They MUST crawl the pages to see the "noindex" meta tags.
That said, categories are generally the lifeline that passes PageRank to deeper content on large sites. If you "noindex" them then you pretty much screw up your site.
Tags, author archives, even date archives can help pass PageRank-like value through a site, too. But they should be substantial before you think about allowing them to be indexable.
Generally speaking, if you don't create many tags it's okay to allow them to be indexed.
If you do create tags and you mix up their use so they are relatively unique compared to each other, it's okay to allow them to be indexed but they can also contribute to a site's being flagged as "low quality".
If people are not clicking on the tags and browsing them, then I would probably not use them.
It's better to redirect tags than to merely delete them, to help improve Website crawl, if you decide to do away with them.
Same goes for categories. If you decide you have too many categories and don't want them indexed, then redirect them and consolidate their content into fewer categories.
The more you block the search engines from crawling and indexing your site's content, the harder it becomes for them to understand your site and ensure that its PageRank-like value flows smoothly throughout the indexable content.

Truslow
Michael covered the technical side of things here pretty well. So I won't go into that. I'll touch on the more nuanced aspects of the choice.
Categories and tags are important because they not only pass the pagerank, but they help give contextual clues to the relationship between documents. Categories tend to be the more broad concepts that your site is going to cover while tags can show relationships between pages that might potentially cross those categorical boundaries.
As such, the tags and categories need to be the RIGHT tags and categories. They need to be used consistently and properly and they need to be done in a way to create structure and relationships between things. If not – then all your category and tag pages are utterly useless – both for the user and Search Engine Optimization (SEO).
If they are set up properly, though… I would contend that they are among the most important things to have indexed (and more importantly followed) on your site because they are things that provide structure, context and connectivity between all the topics you're discussing.
They are also the fallback landing pages for more broad search terms. If someone types something in and Google isn't sure exactly what they want – your category page might be the answer. It can see your site and say, "Okay… any one of these three articles might be what they are looking for, but I can't be sure which one to show. I'm certainly not going to give this site three slots for this search term, but… oh wait… this category page gives them a clear path to all three of the articles, so if I send them there, no matter which one they were looking for, they're presented the options and they can decide! RANK IT!"
There's a lot more to information architecture (and how Google uses that to rank things) than what either Michael or myself have talked about here. These are starting points for something which many colleges offer up as a four year bachelor degree. So it's a pretty big area. You don't need that degree to be able to use it, but you do need to have enough understanding of how it all works to be able to include it in your SEO strategy. So spend some time on it. Learn it and leverage it.

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Lera
I had tested both ways in several blogs. Honestly, there was no notable difference 🤷‍♀️. _👍🏽2

Mew ^👑
Excellent question bud!
As always – it depends. Some of my category pages do incredibly well in the SERPs for news/eCommerce niches.
For local services, absolutely not.
Tags? More so for users than Google. I never see these pages in the SERP unless structured as categories. _👍🏽5
Mišo
If categories are used as part of the website structure, and if they are enriched by additional content, then indexing them is essential.
Many use categories with no plan and without understanding them. Noindexing those is a good decision.
Tags are tricky. You need lots of consistency and thinking it through for tag pages to add value on the SERPs. They are mostly better to be noindexed. _👍🏽3
Doug
I always noindex tags and categories as they don’t offer anything (typically). Although I have seen Charles Float show how you can edit the archive templates for these so that they do actually provide value… so in that case they can be okay. _👍🏽1
Anthony
How about using something like enhanced category page so that you actually use the category page to build up authority for each posts by using unique and useful content. It will provide link juice, push up relevancy, additional pages and hopefully some long tail as long as they don't cannibalize. _👍🏽2
Kolleen
I index Categories because I put a ton of info on the category pages. I don't index tags, ever. I tell my people to stop using them. _👍🏽3
Chris
I personally no-index them. They're fairly useless 99% of the time. Then again, you have a company like Canva who essentially built massive search dominance – with category/tag-like pages. _👍🏽2

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Garcia
To answer your question (and arguably any question for SEO), ask yourself how that page will satisfy the search intent for the keywords and topics you expect it to rank for. If the page literally is a collection of blog posts tagged with that topic but nothing has been done to sort by relevancy or include functionality to find what users are looking for, then you're not going to do well.
Like others have said here, it depends on what other content your have on the site, ability to adjust these pages to really help users, etc. Tag and cat pages could be used only to allow internal link value to be passed but they can also be used to rank if done the right way. _👍🏽3
Phil
If they’re rubbish, noindex them. If they’re really great and helpful, don’t 🙂
Just don’t have dozens of tag pages hoping they’ll rank for all sorts of similar phrases. Those days are gone. _👍🏽2
Eileen
I’ve been planning on implementing what could be considered enhanced category pages on some of my sites that have extensive blog libraries. Basically, the plan is to create unifying SEO-friendly themes, such as New Homeowner’s Guide, adding some unique body content, and linking all blogs with that theme to the new page to help improve UX and shareability. It created quite a bit of havoc on my team. _👍🏽2
Guzman
I have used them both on various sites and there are mixed results.
Can't say indexing category pages have hurt the rankings out otherwise.
Tags, I have never indexed. _👍🏽1
Steve Toth ^✍️
Thanks everyone, this has been super helpful. I've got bigger fish to fry with this client, but I also wanted to illustrate how asking real SEOs is better than reading a blog. I included a lot of these point in my response. Thank you!! _👍🏽1
Noah
I might be late to this one but I typically no index both unless it’s an e-comm site then I leave categories indexable but add some content to them in addition to the listed products _👍🏽4
Krinal
First, check the organic traffic to these pages for a longer time period.
If none of them have any valuable traffic, a quick internal link audit might help. Are there important pages exclusively linked from either of these pages? If so, noindex ing them might eventually mean losing the link equity passed on to pages linked from these pages.
If there is no potential organic traffic or link equity to be lost, by all means go ahead and noindex them. _👍🏽1

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