They can justify what they're doing however they'd like, but I don't think anybody serious believes anything they say. There's a backstory with these people.
Well, I do not consider "serious" countries that are not opposing a genocide because they have neocolonialist interests in the region. Fortunately, we have several serious countries that are acting and also supporting the case in the International Court of Justice.
Different means to the same goal. The Houthis have no access to the ICJ, however they have access to disrupt the maritime trade through the Red Sea, so this is how they act. There is also reasons to believe that even if the ICJ rules in favor of South Africa on Friday, and orders Israel to stop any military activity and let in humanitarian aid, that they will simply not follow it, and there is reasons to believe that USA will excuse this behavior. Disrupting maritime traffic in the Red Sea may proof to be an invaluable action in addition to the ICJ case for stopping the horrors in Gaza.
It is categorically false that the Houthis have the same goal as the ICJ case. One way you know that is that if Ansar Allah succeeded in their chartered goal of liberating Jerusalem and Palestine, they would proceed to bomb all the Muslim Brotherhood's mosques; they seek to liberate Palestine not just from the Jewish people, but from the Sunnis as well. And how you know that is: that's exactly what they're doing, right now, in Yemen.
Of course, another way you know they're full of shit is that they were shooting rockets at cargo ships in the Red Sea years before the Gaza war.
I think a pretty mainstream and reasonable way to look at Ansar Allah is:
What they say: meaningless agitprop about Palestinian liberation.
What they intend: A Zaydi Shi'a imamate with racial and bloodline governance.
What they are: A chaos agent managed by Iran in order to keep Saudi Arabia, which operates a military with one of the world's worst ratios of capacity and funding to competence, perpetually on the wrong foot.
Sorry, stated was implied. These are different means to the same stated goals.
The Houthis are not the only one blocking Maritime trade, there are also activist groups in e.g. Oakland and Tacoma which have blocked freight traffic from respective ports with the aim of disrupting shipment to Israel and the stated goal of stopping the genocide.
What the Houthis and these activist groups in America do after they’ve succeeded in stopping the genocide, that is another question which we can tackle at the time. As of now there is an emergency situation in Gaza, and we must treat it as such. Stopping the genocide is at utmost importance.
That's a horrible thing to say about activists in the US. I may think activists in Oakland and Tacoma are ineffective, performative, and largely wrong in the particulars of their case, but I have never claimed they are morally comparable to Ansar Allah, a racial-supremacist monarchist movement that kills civilians in numbers the IDF has never come close to approaching.
If you support civilian lives then the very last people in the entire world you want to get behind are Ansar Allah. You have to be careful about campism. It's pernicious.