Auron, especially in his younger days, was very moral and idealistic. When he refused to marry the priest's daughter, it was probably because he didn't want to enter into a politicised, arranged marriage - especially not one that would give him prestige among the Warrior Monks, rather than earning it. As Jecht says, he's a real stiff sometimes

I'd say that's the reason - he'd marry for love, not for someone else
s point-scoring.

I agree that the Spheres reveal a lot, though. I would definitely say that Auron, Braska and Jecht love one another dearly, toward the end of their pilgrimage. Auron's deperate attempts to prevent (SPOILER)prevent Braska's sacrifice and Jecht's (SPOILER)willingness to die for his friends' world speak volumes about this.
However, I see theirs as a brotherly love, not romantic.

Of course, Auron's sexuality isn't established in the story; anything is possible.