I comes to mean, "I don't care [about these details]" or "As far as I'm concerned, this is as if ...".
Although it may seem difficult to understand, you can try a with a literal translation
- por mí → as far as I'm concerned
Por mí podemos ir al cine - As far as I'm concerned, we can go to the movies
Comía como si llevase un mes en ayunas - He was eating like he had been fasting a whole month.
So the expression
por mí como si
As far as I'm concerned [I care as little] as if ...
Check Origen de la expresion "me importa un ..." which explains why we often say "I care about this as much as I care for a cucumber", meaning, "I care about this as much as as I care about something of little [monetary] value".
The expression "por mí como si" means that you don't care about something brought to your attention, and you say "well, it could even be this other thing, but I care just the same: nothing". You compare with something to convey "I care as little as if" or "is as unimportant as if"
A wants B to pitty them, or maybe they are just joking ("Oh, poor me. My leg hurts. Please Carry me"). B comes to say "Your legs hurts? Too bad. I would not help/carry you even if you were dying"
A: Me duele mucho la pierna, ¿Me llevas en brazos?
B: No. Por mí como si te mueres. No pienso llevarte.
A claims that some guy (a famous rapper) is a jerk for the way they treat others. B claims that they don't care about it. They are a hardcore fan of the guy and would support them even if they were to beat their own blind and disabled mother.
A: Este tío es un impresentable. ¿Has visto cómo le habla a su mujer?
B: Por mí como si ataca a su madre ciega e impedida. Es mi rapero favorito y le apoyaré aunque dispare y mate al último unicornio vivo.
A says that they have very important customers and they have to be treated well. B claims that they don't care how important they are. The could be members of the Club Coconut, the royal family, or whatever else (Club Coconut sounds like they are mocking some important group or something).
A: Estos son clientes muy importantes. Son todos de la jet set. Hay que dejarles pasar.
B: Por mí como si son del Club Coconut. Acabo de fregar el suelo, y un suelo recién fregado no lo pisa NADIE.
por mí como si lo que sucedió ayer nunca hubiera pasado
This means, "as far as I'm concerned, I'm going to pretend that that thing of yesterday never happened".