Yep, that's the one.
If your hoster doesn't care about spam spreading from their IP space, you should take your mail server elsewhere. There's literally nothing to think about.
And if they do care about this issue, they are likely to be taking steps to remove any of their IP space from the blacklists, without being nudged.
PS.
I've been running a mail server for close to 20 years now and I do blacklist by /24 netblock on the second offense. This doesn't bounce emails though, just tags them as spam. So I had a quick look in the logs and Hetzner, Digital Ocean, OVH and LeaseWeb are all spamming a lot. LayerHost, Colo Crossing, Liquid Web, Host Winds and Servion are also close to the top. Anecdotal data, obviously, so caveat emptor and all that.