If you use the phrase “Jewish people” in your research instead of “Jews”, you will be implicitly adopting the Zionist ideology of Jewish nationalism — or as Shlomo Sand puts it, “the invention of the Jewish people”.
Israel uses the construct of a Jewish people to rationalize the subjugation and ethnic cleansing of non-Jewish Palestinian Arabs, imposing the non-existent construct of an Arab “nationality” on them, in order to further the mythical claims of a Jewish people, by lineal descent, to historic Palestine.
If Palestinians are “generic “Arabs, the Zionist logic goes, they could be displaced to go live elsewhere in the Arab world and be replaced with the “Jewish people”. [See Myths and Facts about Israel/Palestine by Jewish Voice for Peace).
The Zionist semantic ploy in which Israel engages through its definition of “nationalities” within Israel itself also means the absence of an “Israeli nationality”.
In short, the most urgent reason not to use “Jewish people” is because the Zionist construct denies the existence of the “Palestinian people” and leads directly to an apartheid regime in Israel that oppresses and dominates the Palestinian people as a whole.
If you do use it, you should make it clear that you are using the term “Jewish people” to mean ‘Am Yisrael’, an ancient term that refers to a religious (spiritual) and cultural community (like the Muslim umma) that has nothing to do with a political geographic state in Palestine.
Whether one understands Zionism as Jewish messianism realizing itself through a Jewish state or a resolution between “the Jew and the world”, as the Israeli Jewish historian Ben Zion Dinur puts it, Zionism accepts the conceit that the position of Jews in the world is unique — in the sense that they all belong to a diaspora in the world that needs to be resolved — in Palestine’s case, at the expense of the indigenous Palestinian non-Jewish Arabs.
When you refer to Jews, on the other hand, you are referring to people all over the world who follow the religion of Judaism in the same way as you would refer to Christians and Muslims. It is the religion that connects all three groups historically to the Holy Land.
We refer to a “Christian people” or a “Muslim people” only in the sense of identifying them as people who are followers of a religion. I have never quite understood the term “secular Jew”, just as I would find it difficult to understand “secular Christian” or “secular Muslim”.
The construct of, say “A Nation of Islam”, as in the African American political and religious movement, is harmless, because it does not seek, as Israel does, to subjugate others and seize their property. In the same way, we all know how deadly the construct of “Islamic State” is.