As far as I can see a Jew is a decendant from the line of Judea or Benjamin.
There are many people who call themselves jews who are atheist. Many people (jews) in Israel are atheists. In todays terms being a jew has nothing to do with religion at all because many Jews are not religious. And many gentiles convert and did convert to judism who are called jews yet have no lineage or can prove it.
"In today's terms," yes, the restrictive way many want to refer to Jewishness blurs the lines and makes the Bible confusing, especially to someone new in the Faith.
Two tribes, Judah and Benjamin, were part of Judah when that was ruled separately from the rest of Israel. (A rather ugly part of their history, I think) So restricting the word "Jew" away from the tribe of Benjamin makes no sense at all, as you say.
Non-practicing Jews (by birth) have always been held to be Jews. This is significant to our Christian Faith, and should not be changed or removed.
People who practice Judaism, not only Orthodox but also reform, have always been known as Jews regardless of birth; this shouldn't change either. (Very few people who aren't born Jewish convert to Judaism)
Citizenship of the modern State of Israel, and non-citizens living in Israel, maybe aren't Jews since many Muslim Arabs live there now. This is a substantial change from Biblical times, and I think it makes sense for our language to reflect that.
Trying to trace an individual's bloodline to the tribes of Judah and Benjamin is contentious at best, after some 3500 years. Establishing identity on this basis seems ridiculously murky.
"Jew" was originally a derogatory term; maybe practitioners of Judaism want to lose that moniker? I don't think so, since they still strongly relate to the term "Jewishness."