Hi Masonman,
I generally "noindex" tags in Yoast and for really big sites I will also block them in robots.txt (after I know they have been removed from index) - but it depends how you are using them on your site.
Before you "noindex", check GA to make sure your tags pages aren't getting any organic traffic. If they aren't, I would go ahead and set them to "noindex".
If you want to then block them from being crawled, you must wait until the pages have been removed from index. Otherwise, they will remain indexed because the pages can't be crawled and the "noindex" tags won't be seen.
Tags only exist to help users find similar content. You could check GA pageviews for your tag pages to see if people are actually using them - if they aren't, you might decide to stop using them.
You have a few options here...I could give more specific advice on what I would do if I knew more about your site, but I hope this helps!
Cheers,
David