I have gone through a series of perspectives on this matter. You may not agree with me at the end; but I think it's a point of view worth sharing.
The suffix "-ism" can be used to mean different things. "Mongolism" is a physical state, i.e., something real and not merely an ideology. The word "transgenderism" can be used the same way: to refer to a condition that is real, even though it is not physically demonstrable.
That's the sense in which I initially viewed the word. But then it came to my attention that most of the trans people I was hearing refer to this word were interpreting the suffix to mean that being trans is just what you said: an ideology or lifestyle. So, I stopped using it. Subsequently, I have found it useful again, occasionally, when talking to our opponents, because it's the language they use.
Obviously, I believe being trans is real; I'm trans, myself. But our opponents have, without having a clear picture of it, picked up on something real that lies at the heart of our conflict with them.
In virtually all of the discussion on our side, the word "transgender" is used synonymously with "having gender dysphoria"; but these are actually two different things. Gender dysphoria is a verifiable condition with an established treatment protocol; "being transgender" is not. "Being transgender" is how most of us interpret what it means to have gender dysphoria; it's how we explain to ourselves why we are the way we are. But it's just a belief. We cannot prove that gender, as a quality on the male-female spectrum that is potentially divergent from sex, even exists.
So, in a very real way, "transgenderism" can be accurately described as an ideology, because it is an interpretation of the meaning of having gender dysphoria.
Now, do I believe I am "transgender"? I do. I am experiencing something real, and this is the meaning that I give to it. But I cannot prove it. All I can prove is that I have gender dysphoria.
Both sides in this fight conflate having gender dysphoria with being transgender, and it's a large part of the reason we cannot resolve our differences.