I am generally a fan of Cloudflare and I think they are good players and good people, but this is something they really need to fix. The DMCA system is already heavily stacked against the little guy. The least Cloudflare (or any host) can do is listen to both parties. Ideally they should be a neutral arbiter.
I use Cloudflare extensively and spend a lot per month with them, but this really gives me pause about whether I want to have CF hosting my actual content. I've never had a DMCA takedown claim against me, but I know people who have been abused by that process. It can really happen to anyone.
Cloudflare, please don't be part of the problem. You've long been a champion of a more open web, one in which little people can operate. You've done more to enable creators like that than just about anyone I can think of. Please, don't be a facilitator or enabler for the DMCA bullies.