Hugh Hewitt refers to the actor as “center-right” politically speaking, and the actor doesn’t contradict him.
Name recognition is certainly important when it comes to running for office, and so, Matthew McConaughey would certainly have that much going for him if and when he ever decided to run for office.
Whether that would be enough is tough to guess.
Traditionally, Texas has been a “red state” but there have been some apparent inroads made from the left in recent years, so perhaps a center-right candidate is exactly the type who could be the governor one day. So, maybe?