Not trying to defend Oliver Stone or Hollywood in general, but it was the Ancient Greeks who portrayed Alexander as bisexual (bisexuality apparently was common in those days). His successes have nothing to do with his sexuality.
But Alexander was not Greek. He was Macedonian. The Macedonians fought with the Greeks, but they didn't camp together.
But not his contemporaries. The ones who portrayed him as bisexual were writing about him some 200 years later.
Julius Caesar was a notoriously successful womanizer, and yet apparently was a pretty boy who may have been willingly submissive and receptive, should we say, in his purported homosexual life. Thus the famous comment about him: "Every woman's man, and every man's woman."
This was really about power, and not about sex -- the point to the comment was that Julius Caesar was effeminate and weak, and that his "lady's man" image was a farce. It wasn't that he was having sex with men, it was that in those homo relationships, he was being dominated. It was this that was considered to be a disgrace, and that's why his opponents tried to use it against him. I have no idea of whether it was true or not.
I think it very problematic to use classical histories and assume that comments about sexuality can be taken at face value.