Owl Tarot
I always find it odd that people see the Thoth as heavily pushing an agenda, with other decks like the RWS as seeming more neutral, when exactly the opposite is true. The RWS very much propounds Waite's ideas, so much so that modern card meanings derived from the PKT seem to parrot his views on life and morality.
The Thoth does not push its agenda more than any other deck. What it does is speak in a very specific symbolic language which it is useful to understand when working with it. That language is designed to be abstract so that anyone learning it would be able to take it in whatever direction it takes them, from an empowered and informed perspective. That's where "do what thou wilt" comes in, not do what you want, which is what boiling things down generally amounts to.
Kinda like what I said in different words! Everyone could potentially get something out of interacting with the Thoth deck no matter what you may believe (or don't) believe in.
Edit for added content: And the more you read about it's symbols and it's philosophy the more you get for whatever you like to believe in (religiously I mean). I find we are in agreement anyway, since we are saying the same thing more or less. If this posts is directed to mine, please reapproach what I'm saying and you'll see that we aren't saying different things, not am I in disagreement with anyone else on this topic. I'm merely pointing out what I think is interesting, not condeming anything. Overall, I like your post and your approach to "do what thou wilt". It's important not to confuse it with do what you want since the context is different.
Also, I merely said you can go with any belief system as long as you enter the process of learning about the Thoth tarot, which further unites our answers. A little bit of humor: Contradiction exists below the abyss!