As a native Chinese I can assure you 小红书 and 红宝书 are as close semantically to each other as the words constipation and constitution. Few would relate those two.
Even the most leftist Chinese entrepreneurs avoid having their brand names associated to politics; it's just common sense.
> his name is literally Mao
The guy didn't pick the name. "Mao" is the family name he inherited from his father. In the case of Mao Zedong and Mao Wenchao, they have the same family name, but that's about it. The two people aren't even from the same province.
Please, at least learn your lessons first. It's like suspecting everyone with the family name "Manson" to be a serial killer aspirant.
Red is the "good," lucky color in Chinese culture. It's the color of the new year, of weddings, and of other auspicious events
The guy went to university in the US and his name is literally Mao.
He knows Americans call Mao's book the Little Red Book. He back-translated it to Chinese word by word. Anyone who would have an obviously perfect product name like that and not use it would be dumb.
There's zero chance a dude named Mao had an idea for a little red book app and thought "Yeah, I'll call it this because I went to Stanford and they're red." It'd be like Google saying they named themselves after googly eyes and not spelling the number googol differently.