I'd move off Cloudflare. Cloudflare hosts a bunch of sites that are penalized by google. Google is known to penalized sites in bad neighborhoods. Spend the money and get dedicated IPs and don't share certs. Examine.com is sharing a cert with an online gambling site(reengame.com).
Cloudflare is hardly an obscure service. I'm confident that Google's search quality team is aware that Cloudflare exists, and that they have taken steps to avoid penalizing sites for using it.
I thought that as well. Totally anecdotal, but after switching off of CloudFlare and onto a dedicated IP, our rankings increased within 2 weeks. We track algorithm changes through SEMRush, who did not report an algo change around the time the rankings increased. In addition, we actually saw an increase in page load times because the assets were no longer being served via CDN.
https://serverguy.com/case-study/cloudflare-seo/ . It is well known in the SEO arena that your neighbors affect your SERPS. Cloudflare has an open policy on who they allow on their service where AWS, Akmai, Fastly, etc have acceptable use policies banning services like online gambling, online pharmancies, etc.
Google doesn't release any information about how they rank sites but it is reasonable to assume there is a network/IP reputation score similar to what email providers use to combat spam.
I very much doubt that to be an issue. The IP ranges from CF has been classified as CDN by Google back in 2011 [0] to not affect geo and crawl (and reputation?).
BUT, if I would be you I would definitely go for the Full SSL option so you don't share the cert with random other sites on CF.
Of course if nothing else works you can turn off CF to see if anything changes.
