I don't think it matters at all whether your therapist is ABDL-aware or not. The only thing that's important (vital) is that he/she can work
with you (rather than against you) to achieve whatever it is
you want out of therapy.
Client-centred therapy (also known as Rogerian, after Carl Rogers) is a vague model of therapy where the therapist listens to the client, empathises with their situation, and, essentially guides the client through the process of guiding themselves towards recovery (if that makes sense). Or, to put it another way, the therapist guides
you, based on your own ideologies, towards your own solutions/conclusions.
It works with ABDL, because "who you are" is just automatically accepted. "Client-centred" means that, if you don't see it as a problem then it isn't. Or, if it
is a problem, the therapist will guide you towards ways of living that work for
you. Self-acceptance is a fundamental process.
https://www.simplypsychology.org/client-centred-therapy.html
https://en.wikipedia.org/wiki/Person-centered_therapy
Gestalt therapy works well alongside that:
https://en.wikipedia.org/wiki/Gestalt_therapy
Beyond that, look for therapists that specialise in whatever areas might be relevant -- depression, anxiety, relationships, sexuality, drug use, or whatever. Check their professional qualifications.
You should always consider what therapists say with a pinch of salt. They aren't magical soothsayers. They don't know everything that's in your mind (especially if you don't tell them). You have to challenge what they suggest, and in turn they challenge your beliefs. It's a two-way debating process. You shouldn't just accept a therapist who tries to brainwash you into their rigid ideology. But you may find that, when they question your own ideologies... you can recognise a few in coherencies that might change the way you see the world.
The best therapists will be able to pick-and-choose various therapeutic approaches from various psychological ideologies (even conflicting ones), and guide you towards the ones that help you best.
Being honest about your scepticism, thoughts, beliefs, ideologies, etc. is the best (quickest) way to make yourself understood, and let the therapist guide you towards techniques that will help. But you're the one in charge. They can lead you to water, but can't make you drink.
It helps to consider your therapist as an equal; a wise partner or trusted friend who will act as a helpful guide on your journey through the inner-workings of your mind. It's
your journey. The answers are within you. A good therapist will help you see what you already know. He/she will be by your side to support you when you feel lost, and will help you find
your way again.
So... trust what you know... but allow your therapist to question it. Psychology isn't a "hard science" where abstract theories can be proven or disproven. Don't "buy in" to theories that don't work for you.
Dunno if any of that helps, but the best of luck to ya!