If he’s showing signs of jealousy, it’s because he wants you for himself, and his taking you to meet his mother is probably another sign that he wants this to be more of a romantic, traditional relationship and less of a FWB relationship. If he’s introducing you as a friend, the way he introduces other friends to his mother, then this is not a big deal, but if he’s introducing you to his mother because he wants her to know who he’s dating, that’s a sign that he’s trying to leverage this into more than just FWB.
Relationships change all the time, and it’s very normal that a FWB relationship dynamic changes when one person wants more — which pretty much always happens at some point! The question is, what do you want? Can you answer that one?