At first I thought it was just coincidence about playing face of the franchise, but after being locked out of MUT for almost a straight day, I realized that completing an entire storyline in FOTF does remove the MUT human verification. It still returns quickly, but I have consistently been unlocked in MUT every time I finished an entire storyline in FOTF. Sometimes just completing one game finished the storyline, so it wasn't clear until I got to the "dream team" storyline, which covers an entire season. I checked into MUT after playing each game throughout that storyline, and after being locked out of MUT for over a day, I realized it's about completing the storyline and not just a single game in FOTF necessarily. Sometimes I have to reload the computer/origin/game to get the verification to go away, so also consider restarting before you check into MUT each time between games.
Give it a try and if you don't want to play it just autosim and skip through as much of it as you can to see if it works!? Just keep checking back in MUT after each game and see if it goes away.