This is pedantic, but the Mew glitch is when you use the trainer escape glitch to encounter Mew. If you encounter something else with it then it's not the Mew glitch.
For those interested in why this works: it abuses a minor oversight with how the overworld map's event handling is updated, tricking the game into triggering an encounter when you return to the route. When the game tries to read info for the Pokemon you encounter, it reads arbitrary data for the Pokemon most recently battled, because the glitch causes the game to skip the event handler that normally writes over that data.
The species of your encounter will align with the Special stat of the last Pokemon battled, so we just have to battle a trainer with the properties we want, then step back into Route 8 (the map we choose for the glitch). Mew's index number is 21 and the Youngster's Slowpoke has a Special stat of 21 -- and so that youngster became famous.
Clearly, you can pick a different trainer that will load different numbers into memory, causing you to encounter a different species.