If we’re talking Falcon 9, the ignition is using TEA-TEB, a fairly nasty hypergolic. It burns to water vapor and carbon dioxide, plus some boron oxides.
Starship doesn’t use a chemical igniter, so yes, there’s probably a small amount of methane that escapes during ignition. Generally though the combustion for Starship is incredibly clean, with something like a 99.5% efficiency.