That's incorrect:

Marx's family was originally non-religious Jewish, but had converted formally to Christianity before his birth.

If either your mother or father is a biological Jew then you are automatically a Jew by birth. The religion doesn't matter at all, most Jews are atheists. Jews trace their ancestry back to Abraham. Jews are an ethnic group, you can take a DNA test to see if you are a Jew or not.

Jewishness is determined first by blood and second by religion. That is how Jews have done things for thousands of years. You are a Jew, so you know about this, so I don't know why you keep lying so blatantly.