Was a new form of religious participation available to 1st century women as a result of Christianity?
It is sometimes claimed (typically on the basis of later rabbinical writings), that the religious position of Jewish women in the 1st century was elevated significantly by Christ’s teachings, in comparison with the position they had held in Judaism.
Quoting from the rabbinical literature of the Mishnah and Talmud (both compiled long after the 1st century), as if its contents were directly relevant to the position of 1st century Jewish women, has long been criticized by Jewish scholars.
Such quotes are widely recognized as unrepresentative of general 1st century Jewish attitudes,  and create an artificial distinction between Jesus’ attitudes and those of 1st century Judaism.
In fact, there is evidence for the active religious participation of 1st century Jewish women. There is even some evidence for 1st century Jewish women in leadership positions,  contradicting the claim that such positions were only made available to women in the Christian era.  
Inscriptions ascribing synagogue leadership titles to women (once disputed, now accepted), prove 1st century Jewish women were active religious participants in private and public. 
 See for example Wegner, ‘Chattel or Person? The Status of Women in the Mishnah’ (1992).
 ‘Similarly, references to rabbinic customs or sayings as contemporary with Jesus also reflect a misunderstanding of the development of Judaism. The Rabbinate emerged as an institution only after the fall of the Temple in 70 C.E., and it took considerable time before rabbinic authority was consolidated and came to represent more than a minority opinion within the Jewish community.’, Jaskow, ‘Blaming Jews for inventing patriarchy’, Lillith, (11. 7), 1980.
 ‘Ross Shepard Kraemer suggests that ’rabbinic sources may at best refract the social realities of a handful of Jewish communities, and at worst may reflect upon the utopian visions of a relative handful of Jewish men’, Jackson, ‘Jesus as First-Century Feminist: Christian Anti-Judaism?’, Feminist Theology (7.91), 1998.
 ‘In summary, though far from being comprehensive and admittedly insufficient to make my case decisively, the purpose of this note is simply to question the commonly accepted paradigm that women were second-class, unjustly oppressed people in the Rabbinic writings (and some argue, by implication, the OT) and that now, in the new era of the NT, women are finally accorded justice, that is, the same roles as men. Such a position can be argued, citing various chauvinistic Rabbinic sources, but it does not appear that all the Rabbinic data fit this paradigm, and it is even more questionable if the OT, as a whole, can be portrayed as anti-women. More work needs to be done on this.’, Hove, ‘Equality in Christ? Galatians 3:28 and the Gender Dispute’, p. 105 (1999).
 ‘Judith Plaskow (’Blaming Jews for Inventing Patriarchy’, Lilith 7 , p. 11) was one of the first to challenge Swidler and other Christian feminists to deepen their understanding of Judaism before evaluating ’the uniqueness or nonuniqueness of Jesus’ attitudes towards women’.’, Jackson, ‘Jesus as First-Century Feminist: Christian Anti-Judaism?’, Feminist Theology (7.86), (1998).
 ‘She argues for epigraphical, archaeological and nonrabbinic writings to be placed in the total picture regarding Jewish women in the first century: there is evidence ’that at least some Jewish women played active religious, social, economic, and even political roles in the public lives of Jewish communities.’’, Hove, ‘Equality in Christ? Galatians 3:28 and the Gender Dispute’, p. 91 (1999).
 ‘The most compelling evidence comes from Jewish inscriptions from the Hellenistic and Roman diaspora communities. These inscriptions, collected by Brooten and Kraemer,23 appear both in Greek and Latin and date from the first century b.c.e. to the sixth century c.e. Their provenances reach from Italy to Asia Minor, Palestine and Egypt.24 These inscriptions give the titles “Mother of the Synagogue” (μήτηρσυναγωγηˆς, mater synagogae) and “elder” (πρεσβύτερα) to women.’, Crawford, ‘Mothers, Sisters, and Elders: Titles for Women in Second Temple Jewish and Early Christian Comunities’, The Dead Sea Scrolls as Background to Postbiblical Judaism and Early Christianity: Papers from an International Conference at St. Andrews in 2001, p.184 (2003).
 ‘Bernadette J. Brooten argues that ’the inscriptional evidence for Jewish women leaders means that one cannot declare it to be a departure from Judaism that early Christian women held leadership positions.’, Hove, ‘Equality in Christ? Galatians 3:28 and the Gender Dispute’, p. 92 (1999).
 However, there is no evidence that 1st century Christian women actually held such positions, despite their availability; Crawford says ‘early Christian communities produce evidence for the use of the epithets πρεσβύτερα, ’αδεφή [sic] and possibly μήτηρ as titles for women in positions of leadership and authority in the early Christian community’, Crawford, ‘Mothers, Sisters, and Elders: Titles for Women in Second Temple Jewish and Early Christian Comunities’, The Dead Sea Scrolls as Background to Postbiblical Judaism and Early Christianity: Papers from an International Conference at St. Andrews in 2001, p.184 (2003), emphasis added, but provides no definite evidence for adelphē (‘These wives may have participated in various leadership roles in the communities they visited, but Paul does not say this’, p.187, emphasis added), describes the case for mētēr as merely ‘possible’ (p.189), and the earliest evidence she provides for presbutera is from the mid-2nd century (p.190).
 ‘Other women more clearly singled out for their roles as leaders in the synagogues, include Sara Oura, called presbutis, or elder; Beturia Paulla, called mother of the synagogues of Camus and Voluminius, Marcella, mother of the synagogue of the Augustesians; and Simplicia, mother of an unidentified synagogue, whose husband was also called father of the synagogue. Gaudentia is called hierisa, the feminine equivalent of the Greek word for priest.’, Kraemer, ‘Jewish Women in Rome and Egypt’, in Juschka, ‘Feminism in the study of religion: a reader’, p. 227 (2001).
 ‘Until very recently, scholars routinely assumed that women could not have held functional leadership roles in Roman synagogues, and viewed these inscriptions as purely honorific, or, in the case of Gaudentia, evidence for priestly family ties.’, ibid, p. 227.
 ‘Recently, however, Bernadette J. Brooten has convincingly demonstrated that these titles and inscriptions almost certainly testify to women leaders in ancient Roman synagogues. Even stronger evidence exists for women leaders in synagogues in other Jewish communities in the Greco-Roman world.’, ibid., p. 227.
 ‘From these inscriptions, and the adjectives praising their piety and devotion to the law, we see that Jewish women in Rome were active participants in the religious life of their communities, both at home and in the public religious life of the synagogue.’, ibid., p. 227.
 ‘As Brooten has argued, there is no reason to assume that these titles do not reflect a leadership role for the women so designated.25 Brooten lists seven Greek inscriptions that contain the epithet πρεσβύτερα, and Kraemer adds one more.26 The women called πρεσβύτερα appear to have been members of a synagogue council of elders.27’, Crawford, ‘Mothers, Sisters, and Elders: Titles for Women in Second Temple Jewish and Early Christian Communities’, The Dead Sea Scrolls as Background to Postbiblical Judaism and Early Christianity: Papers from an International Conference at St. Andrews in 2001, p.184 (2003).
 ‘From the third century B.C.E. on, large numbers of Jews lived in the Greek-speaking diaspora of the Hellenistic and Roman worlds. Evidence suggests that a number of aspects of Jewish life in these communities, including possibilities available for women, diverged significantly from the norms and prescriptions found in Rabbinic Judaism. While it seems likely that most Jewish women of these milieus lived their lives in the relative seclusion of the domestic realm, Ross S. Kraemer’s examination of funerary and other inscriptions demonstrates that some of them acted independently in social, economic, and religious spheres.24 Kraemer and others have also found evidence for wide ranging female activities in the prominent and diverse roles played by female characters in the Hellenistic Jewish literature of late antiquity, such as Judith, Tobit, Asenath (“Joseph and Asenath”), and in the story of the mother of seven sons (2 and 4 Maccabees).25’, Neusner, et al, ‘The Encyclopedia of Judaism’, volume 3, p. 1485 (2000)
 ‘These positive roles and opportunities constitute Jewish evidence for the significance of women in ancient Judaism.’, Scholer (egalitarian), ‘Women’, in Green, McKnight, & Marshall, ‘Dictionary of Jesus and the Gospels’, p. 881 (1992)