I don't think Israel should accept Arab refugees from their immediate neighbors because A. those countries are more than capable of housing their own displaced population, B. Israel is already dealing with the Palestinians who were rendered stateless by the actions of the Arab League and it's been a mess for nearly a century now, C. Israel is balanced on a demographic knife's edge already, D, none of the populations immediately surrounding Israel are facing genocide. The closest you could argue is maybe Syria, but refugees from there are moving North not South anyway.
Israel has a complicated history regarding non-Jewish refugees facing genocide. I wish they were better about it, but I also understand why they are not (however much I wish otherwise). The best example is the Eritrean refugees who fled to Israel by crossing through Sudan and Egypt and then crossed the Sinai border illegally to claim refugee status. Israel accepted the first wave, but then the Bibi government started calling them 'illegal infiltrators' and built a stronger border fence with Egypt primarily to keep both refugees and Sinai Arabs out of Israel (the latter due to the risk of ISIS attacks).
The Eritrean refugees were essentially dumped in a neighborhood in Tel Aviv and left with no support services. So they got to live, but faced extreme poverty which led to crime, which led to issues of racism against them, cue the Bibi government's hostility towards accepting more. Those who crossed the border after the first wave were basically given the option of claiming they were migrant workers (which meant getting a temporary visa and getting bussed to Tel Aviv) or being held as infiltrators indefinitely in the Israeli prison system until the UN arranged for them to get official refugee status (something that has yet to happen years later). Either way, they were safe from genocide, but Israel was hardly ideal when it came to supporting them and providing a good quality of life. It was a messy situation, exacerbated by issues of racism, crime, and fear of chaos and economic issues if too many Eritrean refugees came to Israel.
Technically Egypt or Sudan should have been responsible for those refugees, but the Eritreans knew better than to trust either of those governments after hearing horror stories of human trafficking (or at least that's what the Eritrean refugees I met in Tel Aviv told me). Thus the Israelis got pissed at the Egyptians for essentially turning a blind eye to Eritrean refugees crossing through Egypt. They also were suspicious of the Eritreans since they waited until they got to Israel (a reasonably safe country) before claiming refugee status. I understand why the refugees waited, but also understand why the Israelis looked side-eyed at both the refugees and the Egyptians because of it.
These days the neighborhoods of Tel Aviv where the Eritrean refugees were dropped off have effectively become slums where the refugees live dozens to an apartment, and the Israeli government looks the other way when it comes to arresting and deporting Eritreans whose work visas have expired. Likewise, they look the other way on several other laws that would effectively prevent the Eritreans from setting up their own businesses. So the Eritrean refugees found a place to live and even set up their own semi-legal businesses to make enough money to survive, but they have not received the benefits and support granted by official recognition as refugees. At some point, this wink-and-a-nod arrangement is going to end, and at that point hopefully the Israelis will either find the Eritreans a safe place to move to or accept them as long-term residents officially. Honestly, I'm not sure what will happen or what the best solution is there.