Can I, as a reviewer, tell authors to get a native English speaker to proofread their paper?
It's obviously appropriate and constructive to comment on writing issues that significantly affect the quality of the paper. The only question is how to do it as constructively as possible.

Personally, I prefer to suggest that "the authors get editing help from someone with full professional proficiency in English" rather than asking for "a native English speaker." I see other reviewers write the latter, so it's not uncommon, but I feel like it sounds a little bit like I'm "punishing" the authors for not having been born in an English-speaking country. There are plenty of academics who are not native English speakers, and don't have the same proficiency as native English speakers, but are still perfectly capable of high-quality academic writing.