Cloudflare is not at all sensible from a privacy standpoint. Cloudflare is a bigger privacy offender than Google and far more detrimental to our rights.
https://git.kescher.at/dCF/deCloudflare/src/branch/master/subfiles/rapsheet.cloudflare.md
Reverse proxying your website through Cloudflare is actually an attack on privacy. You make yourself part of the problem by arbitrarily blocking several demographics of people from your website including Tor and VPN users (people doing their part to retain privacy).
Laziness is what the surveillance advertisers are exploiting. It is everyone’s duty to resist the tyranny of convenience that Tim Wu articulates in a famous essay.
Think of it as boycotting. Exposure of your personal data may not be worth the effort of protecting it, but the big picture is that privacy seekers are not just looking for confidentiality. Privacy is about power and agency. You are exercising your right to boycott a harmful entity. Boycotts are no longer simply a matter of not handing money over, because data is worth money. So boycotting now entails not handing your data over. Giving Google your data feeds Google’s profits.
So you are really asking, “should I give up the boycott”? The answer is no, because the boycott is not just a duty to yourself; it’s a duty everyone benefits from (except Google).