No, the two verses are not contradictory. Gal. 3:26-28 establishes that all who are in Christ are of the same inheritance and are co-heirs because God is no respecter of persons (Acts 10:34)
But, the context of 1 Cor. 14 is speaking of the behavior of both men and women in the assemblies and their uncontrolled, out-of-order exhibitions of speaking with the gifts of the Holy Spirit in the first century AD. There were background cultural issues going on because of the beliefs of Jewish teachings and because of the Greco-Roman treatment of women. 1 2
The Rabbinical teachings of the Jews coming out of the Babylonian captivity during the second temple period rebounded with harsh strictures against women in both assembly and home life, as though by strictly controlling the women, they might avoid any further sins. Maybe the men thought the women were the main reason for their sins of idolatry against God.
The rabbis ruled that women had to sit on separate sides of the assembly, that they could not speak in the assembly, that all singing must be solemn chanting, they were not allowed to study the scriptures, and more. Women were not allowed to speak to men in public, as is still the case in many nations today.
But, Christianity offered women the equality of being co-heirs of the promise, and many women in the early years of the first century held prominent positions and did much for work of the conversions to Christ’s church. On the day of Pentecost, Peter quoted Joel's prophesy of the time of the second destruction of Jerusalem:
And it shall be in the last days, saith God, I will pour out of My Spirit upon all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams; 18 and also upon My men-servants, and upon My maid-servants, in those days, I will pour out of My Spirit, and they shall prophesy; (Acts 2:17-18, YLT)
The pouring forth of the Holy Spirit on the day of Pentecost at the establishment of Christ’s church in approximately 30-31 AD fell upon both men and women, as had been prophesied from Joel 2:28, in a very male-dominated society.
What? came the word of God out from you? or came it unto you only? (1 Cor. 14:36, KJV)
Paul's question was addressed to the men who were prophesying!
And I commend you to Phebe our sister — being a ministrant of the assembly that [is] in Cenchrea — 2 that ye may receive her in the Lord, as doth become saints, and may assist her in whatever matter she may have need of you — for she also became a leader of many, and of myself. (Rom. 16:1-2, YLT)
and on the morrow Paul and his company having gone forth, we came to Cesarea, and having entered into the house of Philip the evangelist — who is of the seven — we remained with him, 9 and this one had four daughters, virgins, prophesying. (1 Cor. 14:36, YLT)
2 Euodia I exhort, and Syntyche I exhort, to be of the same mind in the Lord; 3 and I ask also thee, genuine yoke-fellow, be assisting those women who in the good news did strive along with me, with Clement also, and the others, my fellow-workers, whose names [are] in the book of life. (Phil. 4:2-3, YLT)
These women worked alongside Paul, spreading and teaching the good news to others.
Both men and women are “sons of God” (Gal. 3:26). Both men and women in Christ are of the seed of Abraham and co-heirs of the promise!
and every woman praying or prophesying with the head uncovered, doth dishonour her own head, for it is one and the same thing with her being shaven, (1 Cor. 11:5, YLT)
The women were praying and prophesying in public, and the issue here was that they were to cover their heads when doing so as a sign of subjection to both their husbands and to Christ.
In fact, a close examination 1 Cor. chap. 11 shows the subject is the conduct and manner of dress in the assemblies. 1 Cor. Chap. 14 is an extension of Paul's teachings of behavior in the assemblies. So, the women held a role of praying and prophesying in the first century A.D. in the assemblies as a part of those who received the gifts of the Holy Spirit in that day and time!
You must consider the time period, and that these newly converted Hebrews had suddenly been given new spiritual gifts with which they were learning to contend. They weren’t born with these gifts; they had to learn how to handle them.
If everyone spoke/prophesied at the same time, then there was disorder. If one prophet spoke, the one sitting next to him was to keep still. If those with gifts of tongues (foreign languages) spoke when there was no foreigner attending the assembly, then what use would that be? If there was no interpreter of that foreign language to tell those in the assembly what the tongue-speaker was saying, then no one would benefit.
Likewise, the prophet’s wives - "your women" - were not to interrupt their husbands while speaking in the assembly. But, moreover, 1 Cor. 14:36 is admonishing the men for their tendency to belittle the women as their male-dominated society had been taught to do by their Rabbis. And, that is why the comment about “as also saith the law” is key.
Why would Paul be putting women under the commandment of the law, while preaching throughout his ministry that all of us have been liberated from the law? (Rom. 3:28. 6:14, 7:16, 8:2; Gal. 3:11, 13. 4:15, 5:18; etc) Paul did not quote any scripture in 1 Cor. 14:34-35. Whenever he quoted scripture he typically provided the reference, or said, "it is written." If Paul actually made these statements in 1 Cor. 14:34-35, and there is some question about the authenticity of them, then Paul was quoting back to the men their Rabbinical laws, not God’s law. 3
Again, consider 1 Cor. 14:36, "What? came the word of God out from you? or came it unto you only?“
The word of God did not come from men, nor did it come to them only! Paul could not have been teaching that women should remain silent in church when he had previously discussed the dress and conduct while praying and prophesying in church in chapter 11. If these verses are not an addition by some malicious translator, then Paul was chastising the men for their disparity of women.
The problem in 1 Cor. chap. 14 was the orderly conduct in the assemblies with the misuse of the gifts of the Holy Spirit given to the first-century believers. The whole issue was simply that the wives of the prophets were not to interrupt their husbands during assembly and worship service.
Paul plainly shows in other scriptures that women were deacons, ministrants to the assembly, and workers along with men to teach others outside of the assembly. And, as the women and men were praying in the assemblies as the Holy Spirit moved them, then the women were speaking in "church."
1 Cor. 14:35 does not put women beneath men and does not contradict Gal. 3:26.
Notes:
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During the First Temple period women may have held some sacred offices, but with the final victory of monotheism in Judaism at the beginning of the Second Temple period women were completely excluded from officiating in Jewish cultic practices. Their secondary role in the cultus was exemplified by the existence of a women’s court in the Jerusalem Temple, beyond which women were not allowed to proceed into the Inner Court unless they were bringing a special sacrifice (Josephus, Wars 5:198–9, Mishnah Middot 2:5–6).
Source: Post Biblical and Rabbinic Women
What Role Did Women Play in Ancient Rome
Did Paul Really Say, "Let the Women Keep Silent in the Churches"?