What role does the feminine play in Gawain's identity?
Knights were frequently assigned to guard not only kings and other nobility, but their wives, as well. Knights had a strict code of honor, chivalry, respect, and bravery. They were to protect their lords or ladies at all costs, including being willing to die if necessary.
A year after Gawain accepted the Green Knight's challenge, he lodges with Lord and Lady Bertilak. He makes a deal with Lord Bertilak that each must give the other what he has received that day. While Lord Bertilak is out hunting, Lady Bertilak tries multiple times to seduce Gawain, to no avail. However, Gawain does finally accept a green sash from Lady Bertilak after she insists it will protect him from being killed by the Green Knight.
Accepting this sash from Lady Bertilak was not the right thing to do, and because of it, when he faces the Green Knight, his neck is nicked. He is spared death because he did not give in to the seduction by Lady Bertilak. He is nicked, though, because he accepted the sash and did not tell Lord Bertilak about it.
In this case, Gawain showed great restraint by not giving into the feminine charms of Lady Bertilak.
Like most knights of his day, Gawain was committed to the protection of women and their virtue. That meant he was to protect them from others as well as himself. That particular portion of the code of chivalry was put to the test when Gawain was alone in the castle with Bartilak's wife. She made strong advances toward him, but he resists her at every turn. That's as it should be. He is caught in the unenviable position of revering and esteeming women while rebuffing and refusing the advances of a woman. He's a fine knight and follows the code regarding women. To that extent, then, women are a test of both his manhood and his knighthood.
Some would assume Gawain to have feminine characteristics solely because he is not the typical portrayal of a hero. This is because he is not by any means physically superior, seems to be quite timid, and doesn't walk away with a beautiful dame to end the story, but remember, our idea of a hero may be a bit different than it was at the time this story was written. When the poem was written, Britain was heavily founded on Christian influence. Knowing this, we can assume that their view of a true hero is exemplified by humility and virtue, likened to Christ. Gawain shows his humble spirit after the entrance of the Green Knight when he volunteers to take the challenge even though he claims to be the least of all the knights, only having reason to boast in his relation to King Arthur. His virtue is clearly seen when he refuses to succumb to the continual seduction of the lady at the lord's dwelling. He may fail the first test of bravery with the Green Knight by initially shrugging away, but he does offer his head once more to receive his just consequence, and he returns to his people in meekness, admitting his failures and seeking no praise. Thus, many people come to believe that he is feminine because many of his attributes contradict the strong brave knight that we're all used to reading about, but Christians would have seen him as a victor over the evils of deception and lust, far from the weakness/character of women.