Stonewall said it was reviewing its policies and guidance following the Supreme Court ruling and was awaiting any updates to statutory guidance from the Equality and Human Rights Commission.
The charity added: "Stonewall's guidance has always reflected the law – we regularly review our guidance and work with legal experts to ensure that it reflects the latest legal developments. We will continue to do so."
'Help people explore what is going on'
A spokesperson for Mermaids said the charity "offers support to trans, non-binary and gender diverse young people under 20, their loved ones, and allies of trans children and young people. We do not offer advice of any kind, including medical advice.
"We are here to help people explore what is going on in their lives, how they are feeling, and what might work best for them. We can't, and don't, direct anyone toward a particular decision or path.
"'Social transitioning' can include changing your name and pronouns, updating your wardrobe, experimenting with different hairstyles or beauty products that better align with how you want to express your gender.
"These are things that anyone can do, regardless of gender. Everyone deserves to express themselves freely, including in how they present themselves."
Antoniazzi also told BBC Wales that she agreed with the Equalities Minister Bridget Phillipson that trans women should use toilets according to their biological sex.
She said: "They have a right to be in the men's toilets. They have a right to be safe.
"Gender non-conformity is something we've been used to for years. There is no harm. They should be protected and no abuse should be tolerated at all.
"Everybody should feel safe in the toilets that they use."
