Take chivalry, which has three veins running: the warrior chivalry that centers on loyalty to the king (of which Sir Gawain was the exemplar); the courtly love chivalry that centered on service to the lady and adulterous love; the religious chivalry that centers on righting wrongs and protecting the innocent (Sir Galahad and Sir Percival). They had their compatibilities; a king needed knights to enforce laws and protect the innocent, who often enough were ladies. But they had their competition; warrior vs. religious when the king wants were not just, or courtly love vs. both of the others in adultery. (It's not for nothing that Sir Gawain and the Green Knight centers on a temptation to Sir Gawain's chastity. Adulterous love meant bastards, who either inherited wrongly or lost their positions for their blood which often enough led to war.)
Or bushido. The samurai's military calling conflicted not only with Buddhism's pacifism, but with Shinto's view of blood and death, both of which are held to defile.
And when I was reading (an abridged version of) Mahabharata one woman lamented all the deaths in the battle, only to be rebuked by another woman for views unworthy of their caste; a Kshatriya woman bore sons that they might die in battle, as these men had.
All these are conflicting ideals within a society, not culture clash like Conan the Barbarian's views of the lands that he traveled through. Cultural clashes are rather more frequent in fantasy. Though often enough you have cultures where you aren't really sure what they would consider an ideal.