When it comes to immigration, Israel has a general immigration policy which is a bit strict yet not the toughest to comply with. I'm unsure of the general criteria, but I know it involves residency requirements and an ability to demonstrate an ability to live there. They also have a Right of Return policy, which is the ability for people of certain backgrounds to be fast-tracked to a land considered their homeland. For Jews, Israel is the homeland, and to take advantage of the Right of Return (known as Aliyah) one has to prove that they are Jewish (religiously or ethnically by at least one grandparent).
Refugees are a different issue. Technically speaking, a lot of Israel's populace consists of refugees or their immediate descendants, noting things like the Holocaust and the Jewish Naqba which displaced millions. These refugees are put through programs to integrate them completely into Israeli society and given the ability to rebuild their lives. However, most people often overlook that and only consider non-Jews as refugees, which I get from your question. Things are a bit different with these refugees.
Israel has a lot of refugees of non-Jewish origin, particularly from sub-Sahara Africa. These refugees often come into Israel illegally. Israel can't really be blamed for all of that, since they're much more unwelcome in Egypt and have to pay smugglers to even get to Israel. Egyptian border police is known to shoot them on sight, so shady entry tactics are called for. Once they reach Israel, things aren't perfect but at this point there is a lot more services open to them and they're generally safe. When Israelis find them on their borders, they're taken care of. Given Sudanese and Eritrean origin, they at least know that they're safe from being sent back to their nations of origin given that they lack relations with Israel.
Perhaps Israel can improve its policies on non-Jewish refugees, but honestly you highlight one thing that doesn't paint the whole picture. Governmental services are made available to them and they don't have to conceal their status. A lot of charity is there to make it possible for them to work and have a decent life. They don't fear war and famine in Israel, and threats of deportation are a joke. Furthermore, a lot of Israel's charity is done abroad, and how much Israel gives to those in need on foreign soil is so much given their size and is always ignored.