John Mueller from Google was asked if it is true that Google will remember that a page or site had a noindex directive set. And if it remembers that, even if the page/site removes the noindex, that it will make it harder for that page/site to be re-indexed. John said that is not correct.
Here are those tweets:
That’s not correct.
— ? John ? (@JohnMu) May 19, 2020
Maybe this rumor came out because if you noindex a page or site, then Google might not crawl it as frequently to see if the noindex is still there. But once Google determines that there the noindex directive was removed, Google should begin indexing it quickly.
Google won’t penalize you in the long run for once upon a time having a noindex directive on your site.
Forum discussion at Twitter.