A translation of a recently-posted screenshot for Pokémon Let's Go Pikachu and Let's Go Eevee on the Nintendo Switch indicates players might need to meet certain requirements before they can take on Gym leaders.
The official Japanese site for Pokémon Let's Go updated with new information explaining Gym, Badges, and the mechanics of challenging leaders. That's fine, except Siliconera notes one of the screenshots contains a fellow in a bowtie asking your trainer to show him either a Grass-type or Water-type Pokémon—two types that have an advantage over Brock's Rock-type menagerie. It appears if you don't have one of the asked-for types, you can't pass.
Pokémon Gyms typically have people standing at the entrance to offer you tips on which types of Pokémon will help you in the upcoming battle, but the advisors don't stop you in your tracks if you don't have the "proper" type. Hence why Charmander is considered "hard mode" in the original Pokémon Red and Blue: Fire-types are almost useless against Rock-types, which means you might get curbstomped if you don't prepare carefully before trying to conquer Brock's Gym. We all learned this the hard way back in '98, but it appears Pokémon Let's Go's Gym caretaker doesn't want to see any ten-year-olds die of a broken heart.
It's not clear if your progress will be impeded in a similar manner at every Gym, nor can we even say for sure you won't be allowed to confront Brock without a Grass- or- Water-type Pokémon. So far, there's only one screenshot to base our assumptions off. Pokémon Let's Go Pikachu and Let's Go Eevee are engineered for very young players, but tons of very young Pokémon Red and Blue fans survived learning about Pokémon typing the hard way when Brock's Onix stripped the flesh from their Charmander's bones.
I suppose we'll learn more about this over-protective Gym custodian as we get closer to launch. In the meantime, our Pokémon Let's Go Pikachu and Let's Go Eevee guides have more information than a bowtie-wearing know-it-all stationed outside a Gym door.