Asked again to review a paper, when the authors don't wish to modify it
Personally, I would inform the editors of both journals. For the new editor, I would attach your earlier review, and recommend rejection.

Then it's up to the new editor to decide what to do in this situation. This falls in the category of ethical problems, and I think most journals recommend that reviewers contact the editor immediately in such a situation. Perhaps the journal has a policy for this, or the editor may discuss the matter with other editors or the chief editor.

Let me add why I find it unethical. Peer review relies upon the volunteer labour of anonymous reviewers. Reviewers may invest significant time, and do not really get anything in return. If authors of a manuscript completely ignore reviews, and instead submit an unchanged manuscript somewhere else, I would, as a reviewer, be quite annoyed. At the very least they could reply to the reviews, state point-by-point that they disagree, refuse to change anything and then submit it somewhere else; but completely ignoring is wasting peoples time.