The hospital chaplain [...] is a Quaker. The hospital states that it offers religious support for all denominations.
I said mainstream Christian. Quakers have very varied theological beliefs depending on the individual and the local group they belong to. Calling them mainstream Christian would be problematic. Some groups are, some aren't.
And I bet the clinic offers religious support to its paying customers. It would be more interesting to know how many of those providing the chaplaincy support have the backing of their respective religious authorities.
I didn't read the whole article by the Quaker chaplain, but the abstract makes it clear that it is a polemic against the faith communities who oppose what the clinic offers (gender transitioning for children).