If you're a Cloudflare customer who suffers damages when LaLiga obtains a DNS block for Cloudflare IPs used for pirate streams, you'll have better chances suing Cloudflare for failing to provide the service you're paying them for (of course if you're on a free plan, you don't have much of a leg to stand on).

One Cloudflare customer doing something illegal is only able to cause this much collateral damage because Cloudflare is set up so that taking down one customer requires taking down most of their infrastructure. But what works for DDoS protection doesn't work so well for legally mandated blocks. I think at some point Cloudflare will have to start kicking pirate streams off their platform faster if they want to stay up.

I'm not an ardent defender of Cloudflare by any means, but there is no grounds to sue Cloudflare. Their service is up. Their IP ranges are getting blocked by residential ISPs. How would that be Cloudflare's fault?