I think you can use the Bible to argue, either way.
What matters the most is that inside ourselves we are being modest, not trying to call attention to immoral stuff. But be about Jesus, so this can spread spiritually to others >
"rather let it be the hidden person of the heart, with the incorruptible beauty of a gentle and quiet spirit, which is very precious in the sight of God." (1 Peter 3:4)
It seems to me, how even Christians can evaluate a woman by how attractive she looks, in judging if she is desirable for marriage. This, in my opinion, is judging by appearance, instead of evaluating if she is an example of how Jesus has us becoming and learning how to love. So, if men are judging by looks, they can be missing out on learning how to love, not finding a lady who can help them get real in God's way of loving; and so they are weak so they can break down in close sharing with their wives, giving in to arguing and complaining and bitterness.
So, I think a much more important concern is not only about how a woman shows herself outwardly, but how culture is grooming men to evaluate women by looks and toning of their voices . . . .
My opinion, then, is the topless issue is not what needs to get our attention, so much as how men can be misled about what is love and what is not exactly. Our attention needs, in any case, to stay with personally submitting to howsoever God our Father rules us in our hearts with His own peace >
"And let the peace of God rule in your hearts, to which also you were called in one body; and be thankful." (Colossians 3:15)
I do have some thoughts. Paul does say he became all things to all people, so he could win people to Jesus > 1 Corinthians 9:19-23. So, from this I can see the point of going along with dress codes where the culture and church mores favor a lady covering up. But if I were in a jungle village where people were uncovered, I might loosen up, myself, but still with limits the villagers might not have.
I think I have seen how a woman can present herself seductively, even if she is totally or pretty much totally covered . . . by how she moves, toning her voice, how she can do a little flash of an ankle, or how she might show a bit of cleavage can be enough to get a man going. But a woman's face and hair can be especially beautiful, more than the rest of her whole body, it seems to me.
But the most beautiful are the mature ladies in Jesus love > this gets my attention more, now

> how they can effect me with God's love so I am loving instead of looking.
By the way, the bait you use can be what chooses the fish you catch. I have seen how women can be sassy and dress like they are going to a porn try-out, then they act so aghast that the men they marry turn out to be con artists and cheaters and not responsible and unable to relate well. The bait you use can be what chooses.
You've made a good post. The primary reason that I object to accepting the culture's standard for the sake of testimony
in this case is because men are allowed to go topless. If we tell women that they can't, we're being unchristian through
unfair gender discrimination (there is
fair gender discrimination; this isn't one of those cases.)
In short, we're guilty of being unethical if we don't stand up for women's relatively insufficient rights (or stand
against men's relatively excessive rights). We should pursue equality in this case.
Regarding your comments on beauty: it's true that beauty if fleeting, etc. However, it's acceptable to
also desire beauty:
Ecc 3:11 He hath made every thing beautiful in his time: also he hath set the world in their heart, so that no man can find out the work that God maketh from the beginning to the end.
Deu 21:10 “When you go out to war against your enemies, and the Lord your God delivers them into your hand, and you take them captive, 11 and you see among the captives a beautiful woman, and desire her and would take her for your wife, 12 then you shall bring her home to your house, and she shall shave her head and trim her nails. 13 She shall put off the clothes of her captivity, remain in your house, and mourn her father and her mother a full month; after that you may go in to her and be her husband, and she shall be your wife.
Less direct, but important:
Gen 12:11 And it came to pass, when he was come near to enter into Egypt, that he said unto Sarai his wife, Behold now, I know that thou art a fair woman to look upon:
Gen 29:17 Leah was tender eyed; but Rachel was beautiful and well favoured.
Gen 39:6 And he left all that he had in Joseph's hand; and he knew not ought he had, save the bread which he did eat. And Joseph was a goodly person, and well favoured.
1Sa 16:11 And Samuel said unto Jesse, Are here all thy children? And he said, There remaineth yet the youngest, and, behold, he keepeth the sheep. And Samuel said unto Jesse, Send and fetch him: for we will not sit down till he come hither.
1Sa 16:12 And he sent, and brought him in. Now he was ruddy, and withal of a beautiful countenance, and goodly to look to. And the LORD said, Arise, anoint him: for this is he.
1Sa 16:18 Then answered one of the servants, and said, Behold, I have seen a son of Jesse the Bethlehemite, that is cunning in playing, and a mighty valiant man, and a man of war, and prudent in matters, and a comely person, and the LORD is with him.
2Sa 13:1 And it came to pass after this, that Absalom the son of David had a fair sister, whose name was Tamar; and Amnon the son of David loved her.
2Sa 14:25 But in all Israel there was none to be so much praised as Absalom for his beauty: from the sole of his foot even to the crown of his head there was no blemish in him.
1Sa 17:42 And when the Philistine looked about, and saw David, he disdained him: for he was but a youth, and ruddy, and of a fair countenance.
1Sa 25:3 Now the name of the man was Nabal; and the name of his wife Abigail: and she was a woman of good understanding, and of a beautiful countenance: but the man was churlish and evil in his doings; and he was of the house of Caleb.
1Ki 1:1 Now king David was old and stricken in years; and they covered him with clothes, but he gat no heat.
1Ki 1:2 Wherefore his servants said unto him, Let there be sought for my lord the king a young virgin: and let her stand before the king, and let her cherish him, and let her lie in thy bosom, that my lord the king may get heat.
1Ki 1:3 So they sought for a fair damsel throughout all the coasts of Israel, and found Abishag a Shunammite, and brought her to the king.
1Ki 1:4 And the damsel was very fair, and cherished the king, and ministered to him: but the king knew her not.
1Ki 1:5 Then Adonijah the son of Haggith exalted himself, saying, I will be king: and he prepared him chariots and horsemen, and fifty men to run before him.
1Ki 1:6 And his father had not displeased him at any time in saying, Why hast thou done so? and he also was a very goodly man; and his mother bare him after Absalom.
Est 2:7 And he brought up Hadassah, that is, Esther, his uncle's daughter: for she had neither father nor mother, and the maid was fair and beautiful; whom Mordecai, when her father and mother were dead, took for his own daughter.
Job 42:15 And in all the land were no women found so fair as the daughters of Job: and their father gave them inheritance among their brethren.