I painstakingly went through each Metal Gear game to figure out which Muppet should be which character. I went pretty obscure for a few of them, so here's a list of who's who in each picture, along with a link to both the appropriate Muppet Wiki and the Metal Gear Wiki pages.
Muppet Gear Solid
Muppet Gear Solid 2: Tadpoles of Liberty
Muppet Gear Solid 3: The Muppets Take Mother Russia
A generic Muppet - Volgin
Muppet Gear Solid 4: The Great Patriot Caper
Muppet Gear Solid 5: The Rainbow Connection
A generic Muppet - The Man on Fire