Fashion is something we deal with every day：从句（that）we deal with every day 做表语补足语.
Even people who say they don't care what they wear choose clothes every morning that say a lot about them and how they feel that day.：
主句：Even people （who say they don't care [what they wear]） choose clothes every morning,括号里的复合从句是一个定语从句,修饰先行词 people；而这个定语从句中还有个宾语从句 what they wear.
后面的从句 that say a lot about them and [how they feel that day]：我认为这是一个和主句并列的句子,其主语是主句的主语people.引导词 that 应该是 and 的误置.其中括号部分是 say的宾语从句.