My 11 Might Renekton, Brute is disempowered by my own Profiteer. What happens when my opponent plays Stupefy choosing him? Will his ability trigger? What happens if instead I activated his ability?

Renekton’s ability will not trigger in either scenario.

In order to “become 10 or more,” his Might would have to have previously been less than 10. “10 or more” is a state, and Renekton’s triggered ability checks for the event of him achieving that state. If he maintains that state, regardless of how his Might changes, he will not “become” that state.