Misty from the Pokémon anime came under a lot of fire when her character went from complete Tsundere to more motherly upon obtaining Togepi; the jury is still out on whether it's legit character development or lazy writing, but a lot of the criticism levelled at her is pretty unfair. Being motherly towards Togepi didn't make her any less of a competent Pokémon trainer.
Being caring towards her Pokémon is a strong character trait in Misty's case: a good example is the episode where we learn how she tamed her berserker Gyarados: by taking a Poison Sting for it during a battle with a bunch of rogue trainers. And Togepi, being a baby Pokémon, logically needs more care than average. Maybe it wasn't well-written, technically speaking, but it's not that farfetched.
Plus, even before Togepi she displayed motherly qualities, most notably towards the Horsea she rescued in Tentacool and Tentacruel and later Jigglypuff when they first found it.
May and Dawn have also been bashed for being girlier than Misty and being Coordinators rather than full-time Pokémon trainers or breeders. Never mind that there are several male Coordinators like Drew and Harley. Harley himself is shown to have◊ EXTREMELY archetypically girly traits◊ in canon, but he's "allowed" to have those without having fans bitch him out whereas May is bashed and hated for being more or less feminine.
Then again on another note, due to how quickly she dealt with Mamoswine, Dawn might actually have more potential as a trainer than Ash. And she's the first dress-wearer...
When Pokémon Black and White was released, Fanon immediately labeled the female PC as a confident tomboy with plenty of battle prowess. When it came for Pokémon Special came to adapt the games, fans bashed the PC's counterpart, White, as she turned out to be a Neutral Female with no knowledge of Pokémon battling. Never mind that:
1) It was still early in the arc with plenty of time for her to grow into a proper Action Girl. Yellow and Platinum didn't start out as badasses.
2) She has a full time job that doesn't leave her room for Pokémon training.
3) Said job is actively running her own business, an impressive feat for a girl in her midteens.