Proto-Christians, would-be Jews, ultra-observant Jews or something else?

Christian scholarship posits that there was a group of proto-Christians who called themselves "θεοσεβιοι" God-fearers.  According to Christian scholarship, these proto-Christians were in the early trajectory of Christian development--Jews ⇒ Jewish Christians/Christian Jews ⇒ Christians.  Jewish scholarship opines that θεοσεβιοι were a sect of Jews who were dedicated to the "most high G-d" (as opposed to the ordinary G-d).

These are interesting hypotheses.  They are, however...inaccurate.

We know of θεοσεβιοι from inscriptional evidence:  specifically, from inscriptions found in the amphitheatre at Miletus, where seating sections were designated ιυοδαιοι και θεοσεβιοι--Judeans and theosebioi.

The Christian theory derives from a desire to locate early Christianity within ancient Judaism.  The Jewish theory derives from a desire to reflect ancient Jewish denominationalism (in which case, the θεοσεβιοι would be a sort of ancient world-חסדים).

There is a possibility that is neither of these theories.  It is possible that the θεοσεβιοι were non-Judeans Greeks who became enamoured of Judean "philosophy" (via the LXX), who wanted to participate in the Judean philosophical "cult," but who did not want to submit to the surgery necessary to become fully-participating members of that cult.

It should be noted that throughout history, the sole sign of Jewishness (in the ancient world, of being a fully-participating member of Temple worship at the Temple in Jerusalem, and the other Temples that operated according to the rules of the Temple in Jerusalem) was the possession of a circumcised penis.  For this reason, women, in the ancient world, were not considered "Judean" in the sense in which we now understand Jewishness--for the simple reason that women lack penises to circumsize.  This is also the reason that Ezra/Nechemia inveigh against marrying "foreign women"--foreign women might (would probably) bring their foreign gods and the worship of those foreign god into the marital home. A non-foreign woman (a woman born into a family where the sole worship was of the G-d worshipped at the Temple in Jerusalem or one of its affiliates) would not present such a difficulty.

We know the Greco-Roman world interested itself in "foreign philosophies," a in foreign cults.  We also know that the Greco-Roman world prized the body, specifically the male body, and valued it in its whole state.  This means that circumcision would present a problem to Greco-Roman males who read the LXX and who wanted to participate in the Judean "philosophy" cult.  The Greco-Roman aversion to surgical interference with the male body would mean that those males who wanted to participate in the Judean cult would not be permitted to do so.  However, those who read the LXX and wanted to follow its "philosophy" without undergoing the surgery necessary to be a fully-participating member of the cult could do so under the designation of θεοσεβιοι--those who "fear" the G-d of the Judeans, but who are not fully-participating members of  Judean Temple cultic worship.