I say, and with God's success: The prayer is valid while wearing shoes if they are clean, but because of this, one cannot perform some of the Sunnah acts in prayer, such as the way of sitting in a manner of spreading the legs, and directing the toes towards the Qibla during prostration and sitting; therefore, one would be at fault for neglecting the Sunnah, and their action would be disliked as a matter of etiquette for neglecting the rightful acts; thus, it is better for them not to pray in them except out of necessity, and God knows best.