Blue being our rival he should pick a starter Pokémon with an advantage over our Pokémon right?
But how could Blue have a Blastoise if Red has a Bulbasaur?
The anime is a completely different thing from the games. I'm going to list multiple scenarios blue probably picked Squirtle 1. possibly because it is blue? still a possibility, though it is disproven by Red having a Bulbasaur. 2. Blue could have possibly wanted a bigger challenge. so instead of choosing Charmander, he chose Bulbasaur.
3. The creators may have wanted Red to have a type advantage against his rival, so they made him pick Squirtle.
4. Charmander could have possibly already been taken and Bulbasaur was the one left. As seen in the game, there is only one Pokemon left. 5. Blue/ Red liked the Pokemon the most and decided to pick it, no matter what the type. and finally 6. Red could have been there after Blue and chose the one with the advantage.
that's all my hunches I have and I hope this would answer your question.