I don't think you understand Normalise?
Normalize makes all moves used by the Pokémon with this Ability act Normal-type instead of its ordinary typing.
Normalise only affects the moves used by the Pokemon. The Pokemon could be any type. It just so happens that the only Pokemon that have this ability is Delcatty/ Skitty, and they're normal types.
Normalise affects nothing else apart from moves used by the Pokemon with the ability, so Delcatty would still be weak to Fighting and immune to Ghost, with no resistances.