We know that it is okay to have sponsored content on your site, in fact, Google says in its news publisher guidelines is acceptable as long as it doesn't exceed your primary content and is not mislead as editorial content. Google's webmaster guidelines add that you need to nofollow links on content that is sponsored.
Google said on its webmaster channel on Twitter that you do need to nofollow external links on sponsored content but you do not have to block Google from indexing that content. Google said that "If you don't mind that this content is seen as a part of your website, then just using rel=nofollow would be suitable. If you don't want it seen as a part of your site in search, using noindex would be better than robots.txt."
Here is the tweet:
Hi again, Dan! That's correct. If you don't mind that this content is seen as a part of your website, then just using rel=nofollow would be suitable. If you don't want it seen as a part of your site in search, using noindex would be better than robots.txt.
— Google Webmasters (@googlewmc) August 26, 2019
Here is the link guidelines that say "Advertorials or native advertising where payment is received for articles that include links that pass PageRank" need those nofollow attributes if you have external links.
Here is the Google News publisher guidelines that say "Advertising and other paid promotional material on your pages should not exceed your content. We do not allow content that conceals or misrepresents sponsored content as independent, editorial content. Sponsorship, including, but not limited to, ownership or affiliate interest, payment, or material support, should be clearly disclosed to readers. The subject of sponsored content should not focus on the sponsor without clear disclosure."
I see many SEOs and even old-time SEOs confuse this, espesially on the Google News publisher side.
Forum discussion at Twitter.