My quibble with OP is that he’s using “anti-democratic” to mean exactly the opposite. The concern is not that a minority of voters will force countries to exclude climate refugees. To the contrary, the concern is that a majority of voters will seek to exclude refugees, in contravention to, as you put it, migrants’ “rights.” But who decided those rights exist? Most people in the world would not agree anyone else has a right to live in their country. Even insofar as they might welcome refugees, they would see that as an act of magnanimity, not “rights.”
Whether or not Hungary meets this definition in 2022, however, is an open question.
What I meant was that our ideas of due process and equality before the law will be seen as much less desirable when those things will be the obstacle to deporting large numbers of refugees. Those things are also fundamental to democracy.
You might find Shadi Hamid’s writing on illiberal democracy interesting: https://wisdomofcrowds.substack.com/p/first-draft-is-there-a...