People who become MMA fighters usually start out learning one style first. As the sport has progressed over the years, teaching people how to mix different styles together has changed. Now, with more experienced teachers, students benefit as techniques and teaching methods evolve.
My first combat style was boxing. I was trained to fight with left foot forward, to pop the jab and throw a hard, straight right. Plus, other combinations, of course.
Jiu jitsu was next. I didn't think about which side to use, I automatically followed my boxing stance. Most of my moves start on the left in order for me to follow through with my stronger right side. We were encouraged to drill both sides to develop body memory when you get caught in a bad position.
Kick-boxing classes allowed me to practice throwing kicks, knees and elbows. I still favored the orthodox stance, even though, by that time, my teachers were encouraging me to practice switching stance. This complicated things because defense has to switch to accommodate where my opponent is standing. We either both fight lefty or both orthodox or a mix of the two. That makes a huge difference.
The first time I tried drilling punches as a lefty against a training partner in orthodox stance, I was alarmed at how close my opponent was to me.
My coach explained the difference in positioning and we drilled offensive and defensive moves to handle fighters who switch stance as the fight progresses.
Wrestlers approach straight forward. That scary speed and heavy pressure happens too fast for a person to choose a side, left or right. You have to rely on body memory and hope your choice allows you to maintain a strong base and stay standing. Or else, hit the mat and work your jiu jitsu.
My wrestling single-leg or double-leg take downs are always going to favor my strong, right side.
So, that's my pattern. If we ever spar together, you'll figure out which side I favor. On your side, if I see elements of other fighting styles, then I either stick to what I know or relish the opportunity to practice switching from right to left, just to see what happens.
Karate, Kung Fu and TKD fighters use both stances to throw strikes wtih ease and speed. There's always something new to learn when you spar with someone who has different training from you. That's what makes it fun.
Related Question: Is the differentiation between southpaw and orthodox stance useful?