Leaving the "heavy lifting" of researching and citing various authorities on sex roles of the first century to people more competent to do so than I, I will limit myself to giving a gospel overview of Jesus' interactions with the fairer sex in His earthly ministry.
Jesus challenged the status quo quite frequently, not just in obviously "religious" issues of the day, but also in tangential issues, such as the disparate roles of men and women in both religious and cultural contexts.
That Jesus would engage a woman in conversation, for example (John 4), was truly unusual at the time (Jn 4), and His disciples were taken aback at Jesus' breaking of such a cultural taboo. John tells us Jesus' disciples were "amazed that He had been speaking to a woman" (and a Samaritan woman at that, given the antagonistic relationship between Jews and Samaritans at the time; see John's explanatory comment in verse 9).
The disciples did not realize that whereas earlier they had been commanded not to take their kingdom message to any city of the Samaritans but to only Jews (Ma 10:5), the same "rule" did not apply to their Master, because He had a divine appointment to introduce the kingdom of heaven to the despised Samaritans. Why? Because "He had to pass through Samaria" (v.4).
Jews of that day would skirt Samaria entirely as they journeyed "up to Jerusalem," so as not to become ceremonially unclean by, heaven forbid, bumping into a "half-breed" Samaritan. Not so Jesus. His message of love and forgiveness was to all humankind, not just His own "kind," who by and large rejected Him and His message (see Jn 1:11, "His own . . . did not receive Him").
That Mary felt free to be at Jesus' feet was indicative of her Lord's "open door" policy with women, even though women were considered third-class citizens at the time. Evidently Jesus had set some sort of precedent that gave Mary "permission," as it were, to position herself physically at Jesus' feet.
Remember, Jesus loved "Martha and her sister and Lazarus" (11:2 and 5), and on more than one occasion stayed at their home in Bethany. Even the apostle John gets in on the act of sexual equality, so to speak, by saying that Bethany was "the village of Mary and her sister Martha" (11:1) and that the house He entered was "Martha's home" (Lk 10:38)! I would venture a guess that a Jew in those days would describe neither the village nor the house of a woman as the abode of "Mary and her sister Martha," but rather the abode of the man Lazarus!
Luke also informs us that in addition to the Twelve, "some women" (8:2 and 3) were with Jesus as He traveled "from one city and village to another" (8:1). Moreover, it was women such as Joanna, Susanna and "many others" who supported Jesus and His disciples financially "out of their private means" (v.3). In short, Jesus was anything but a sexist in the way he recognized women to be fully equal to men, while at the same time showing due deference to the weaker sex (see Jn 19:26 and 27).
I find it interesting that in Matthew 12, Jesus, after asking the question to the crowd of people "Who is my mother and who are my brothers?" followed up His question with the statement, "For whoever does the will of My Father who is in heaven, he is my brother and sister and mother" (v.50, my emphasis). In other words, there are not just brothers in the family of God, but mothers and sisters, too!
In conclusion, while neither Jesus nor later his disciples did not obliterate all cultural male-female distinctions in their day, they did recognize the inherent equality of the sexes in the eyes of God. In Christ, there is no male or female (Ga 3:28). In the church of Christ, however, there were and are somewhat distinct roles for men and women, which we need not delve into now.
Clearly Jesus was eons ahead of His time in recognizing the inherent worth of women, not to mention children, too, both boys and girls, of whom He said, "Permit the children to come to me, and do not hinder them, for the kingdom of God belongs to such as these" (Lk 18:16; Mk 10:14; Mt 19:14).