What religion can survive the criticism it would level against another religion?

In order for a religion to “prove” itself—in order for a religion to disprove its competitors—it must undertake a criticism of other religions. Christianity is not intellectually compatible with Judaism, and vice-versa. Thus, to win converts, Christianity must disprove the claims of Judaism, and vice-versa. And the same is true for Muslims. And Hindus.

How, therefore, does any religion disprove another while at the same time proving their own religion?

It’s an absurd conundrum, because every religion suffers from the same critical flaw—none of them have any proof.