So yeah lets say somebody was making a mono blue team would a shiny Mew be eligible? (shiny Mews are blue)
It depends on who you battle. I for one have it be the color of the Pokemon according to Bulbapedia's ColorDex. However, another person could say that shinies are okay. I go with ColorDex only due to the fact that if people are left to their own interpretations of color for Pokemon, it can easily get messy.
The Monocolor format in Pokemon Showdown! uses the official Pokedex color for HOME, which does not assign shinies colors separately. Hence, if you're using a Mono Red team and were to use Shiny Scizor (which should be considered yellow not red), that would still be valid because regular Scizor's color is red. Unfortunately, that means you can't use Shiny Mew on Mono Blue teams and it must be used on Mono Pink teams, as that is regular Mew's dex color.
It depends on what they would accept. I know I would. :)