I'm red, but I can also be blue
humans have red blood, but nobles were sometimes referred to as having blue blood because they never went outside
When in a lizard, I might be green
some lizards have green blood
I'm thicker than water,
and I have a slightly higher density.
"Blood is thicker than water"
I have to do something with a monkey,
but the connection might be negative
Rhesus factor (Thanks, @RadoslavHristov!)
I symbolize both life and death
You need blood to live, but bloody is often negative and connected with death