The ESV offers a good essentially literal translation, rendering the verse this way:
But the Jews incited the devout women of high standing and the leading
men of the city, stirred up persecution against Paul and Barnabas, and
drove them out of their district.
Looking at the following items I found, I think that we can conclude that Luke is describing women who were religious and well respected in Antioch in Pisidia.
First let's look at some of the key Greek words and their translations to set the stage.
Jews - Ἰουδαῖος
2453 Ἰουδαῖος [Ioudaios /ee·oo·dah·yos/] adj. 198
occurrences; AV translates as “Jew” 193 times, “of Judea” three times,
and “Jewess” twice. 1 Jewish, belonging to the Jewish race. 2 Jewish
as respects to birth, race, religion.
devout - σέβω
4576 σέβω [sebomai /seb·om·ahee/] v. Middle voice of an apparently
primary verb; 10 occurrences; AV translates as “worship” six times,
“devout” three times, and “religious” once. 1 to revere, to worship.
high standing - εὐσχήμων
2158 εὐσχήμων [euschemon /yoo·skhay·mone/] adj. Five occurrences; AV
translates as “honourable” three times, and “comely” twice. 1 of
elegant figure. 1A shapely, graceful, comely, bearing one’s self
becomingly in speech or behaviour. 2 of good standing. 2A honourable,
influential, wealthy, respectable.
leading (men) - πρῶτος
4413 πρῶτος [protos /pro·tos/] adj. 105 occurrences; AV translates as
“first” 85 times, “chief” nine times, “first day” twice, “former”
twice, and translated miscellaneously seven times. 1 first in time or
place. 1A in any succession of things or persons. 2 first in rank. 2A
influence, honour. 2B chief. 2C principal. 3 first, at the first.
I looked at a few commentaries that emphasize textual criticism and I found this item that gives a good view of the women mentioned here:
The devout and honourable women —female proselytes of distinction,
jaundiced against the new preachers by those Jewish ecclesiastics to
whom they had learned to look up. The potent influence of the female
character both for and against the truth is seen in every age of the
Jamieson, R., Fausset, A. R., Fausset, A. R., Brown, D., & Brown, D.
(1997). A commentary, critical and explanatory, on the Old and New
Testaments (Ac 13:50). Oak Harbor, WA: Logos Research Systems, Inc.
Pulling all of this together we can see that the women referenced were clearly the faithful and religious ones in their city. Antioch in Pisidia had a large Jewish (as a nationality or race, although assumed to be very religious) population and it is a little unclear whether this references Jews, Gentiles, or both. The Greek word "kai" used for "and" implies that the Jews who were stirring up trouble were using the men and the women both. As to what role the women specifically played, this passage is not clear. I would not assume that they brought this to the attention of the men who then acted upon it, although that is possible from the text.
Strong, J. (1996). The exhaustive concordance of the Bible : Showing every word of the text of the common English version of the canonical books, and every occurrence of each word in regular order. (electronic ed.). Ontario: Woodside Bible Fellowship.