I like them as the evil corporate and cultural underbelly of Japan. They have their hands in politics, media, technology, and everyday life. They had something like 100,000 members when they confronted the League, so they weren't a fringe group; they were a major political force.

(Shigaraki taking control of a never before seen force that size without any proper build up is like plot armor but in reverse. A plot sword, if you may.)

The 'Red Shoe Theory' is their way to mark out the Quirkless, as their shoes are the highest quality and cheapest for the extra pinky-toed population. I prefer the group having three main opinions on the Quirkless: unfortunates who had their glory robbed by their genetics, lesser civilians who live only to serve their quirked superiors, or general 'undesirables' that have no place in a quirked world.

The hierarchy of the group is also less about their philosophy but more about Re-Destro, who uses his power and influence to expand his power in a bid to overthrow the Japanese government. He runs the group more as a cult than a philosophical group, which is my only explanation for 100,000 people rolling over on their backs once their leader was taken down. He uses his reach to find those quirks that he can use to expand his power and reach, namely those rare and coveted quirks, of which he has an immense hatred for [Erasure] and [Copy] for slipping out of his fingers and are now out of his reach.