How did Christ s interaction with Mary and Martha (Luke 10:38-42) change how women were treated in biblical times?

This shows us how Jesus treated women differently to the norm, in His ministry. He showed great respect for the rights of women to learn the things of God, not restricting His teaching just to the men. He addressed crowds of men, women and children equally. He encouraged Mary to learn from Him and exhorted Martha to do likewise.

Martha was upset because her sister chose to learn from Jesus instead of helping her prepare a meal. But Jesus gently pointed out that Mary had made the right choice. "Only one thing is needed," Jesus told Martha, and that what Mary had chosen would not be taken away from her.

Martha would have been shocked, for Jesus pointed out that He knew how many worries and concerns she had, but still He did not exhort Mary to help her. Martha needed to deal with her anxieties by doing the one needful thing, stopping to sit at Jesus' feet and to learn from Him.

That does not just apply to women! However, it does show that Jesus encourages women to shelve their kitchen tasks in order to learn from Him. Those domestic duties will still be there after they have listened and learned. Jesus said elsewhere that we are not to fret about food and clothing as each day has trouble enough of its own, so we take one day at a time. God provides the necessities for those who put Him first.

So, this is about priorities. I doubt if women back then were treated any differently other than by Jesus and His followers who heeded His example. Certainly in the new Christian gatherings the women joined in as equals in Christ, even though the men fulfilled their God-given responsibility to do the teaching, but women had the green light from Jesus to leave the kitchen and learn of Him! That was radical!

Jesus teated his cousins with love, sensitivity and respect. Lazarus, too.

Gen 3:16 Unto the woman he said, I will greatly multiply thy sorrow, thou shalt bring forth children and thy desire shall be to thy husband, and he shall rule over thee.

Ephesians 5:22 - 24:

22 Wives, submit yourselves unto your own husbands, as unto the Lord.

23 For the husband is the head of the wife, even as Christ is the head of the church: and he is the savior of the body.

24 Therefore as the church is subject unto Christ, so let the wives be to their own husbands in every thing.

Corinthians 14:34-35.

34 women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the Law says.

35 If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church.

1Ti 2:11 Let the woman learn in silence with all subjection.

1Ti 2:12 But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.

Almost certainly it did NOT change that

except perhaps within the relatively small Christian community that existed in Biblical times.

Since that is only a "perhaps"

the question would appear to be moot.