If you're going to define your movement as anti-genocidal you should really have a firm grasp on what genocide is and who is committing it:
Article II of the Convention defines genocide as:
... any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:
(a) Killing members of the group;
(b) Causing serious bodily or mental harm to members of the group;
(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;
(d) Imposing measures intended to prevent births within the group;
(e) Forcibly transferring children of the group to another group.
Hamas, what Israel has been clear they intend to destroy, is not a national, ethnical, racial or religious group. However, Jews/Israel/Israelis, what Hamas has been clear they intend to destroy, are. Therefore, legally Oct 7 was an act of genocide, and Israel's war on Hamas is not. Such a designation has nothing to do with body count.
I support Israel because I oppose the genocidal. Binding their hands and preventing them from retaliating in self-defense only serves to support genocidal Hamas by keeping them in power.