As fun as it is to analyze 8-bit era video games which are obviously not designed for such things, let's not get carried away here.

First of all, Mario would fall under the category of "silent protagonist". It's generally hard to ascertain the sexuality of one such character, since, well, they kind of never say anything, you know?. They also tend to act fairly neutral. In RPGs and platformers alike, they usually represent the will of the player, and nothing more. And in a platformer, that is usually limited to "finish level get points". It wouldn't be fitting for Mario to speak while engrossed in saving a princess, he never has, why should he start now?

And that's another good point. If he's gay, you'd think he wouldn't spend so much time trying to save the embattled princess(es). He must have some affection for them if he'd go to such lengths to save them from Bowser.

Also, I don't think Nintendo, who is known for being particularly conservative with the content of their North American releases, would be willing to portray a gay main character. In fact, I don't think any aspect of Mario's personality or biography besides his occupation as a plumber was on the Nintendo devs' minds when they were creating him.

Finally, I think the ill-fated dream in Super Mario Borthers 2 can safely be attributed to psychoactive mushrooms. Who knows what you'll dream when you eat some of those? Again, that was obviously not Nintendo's intent, but we threw that out the window a long time ago with this node, didn't we?