[SauronOfMordor]

but people with jewish mothers would be jewish to jews and raised as jews -

My sister-in-law was born Jewish, converted to Christianity, married a Baptist, raised her two daughters as Christians, and the oldest just married a Christian.

Would you consider them Jews?

[SJackson]

My sister-in-law was born Jewish, converted to Christianity, married a Baptist, raised her two daughters as Christians, and the oldest just married a Christian.
Would you consider them Jews?

No, she's Christian. Which is not to say she couldn't lie about the conversion, in which case she's Jewish if born to a Jewish mom.

From Law of Return 5710-1950

For the purposes of this Law, "Jew" means a person who was born of a Jewish mother or has become converted to Judaism and who is not a member of another religion."

[Alouette]

My sister-in-law was born Jewish, converted to Christianity, married a Baptist, raised her two daughters as Christians, and the oldest just married a Christian.

Would you consider them Jews?

They are Jewish according to halachah (Jewish law). Should they at some future time decide to become Jewish, they would technically not have to go through a formal conversion. However, if they practice Christianity, and identify as Christians so practically speaking, they are not Jews.