Is it permissible to pray in a shirt bearing the logo of a company that engages in unlawful activities, especially given that it has been prayed in numerous times already?

"Mixed martial arts" are forbidden because they involve striking the face and inflicting harm, and it is impermissible to promote them. It is not permissible for a Muslim to wear clothes that promote these forbidden sports, whether in prayer or otherwise. As for the validity of prayer, whoever prays in forbidden clothing, their prayer is valid with sin if they knew the ruling, because the prohibition of the clothing is not specific to prayer.