Interesting question
For the ideology part we look to the definition of ideology "a system of ideas and ideals". Given that many would sum up trans ideology as the idea that each person has a gender identity or sense of gender which may not align with biological sex, I think it meets the criteria. There is no factual or scientific evidence that support this, thus it is an ideology.
For the Cult bit, it's a bit more difficult as it depends whether you go with the traditional meaning of Cult - a group usually led by a chiasmatic, self-appointed leader who tightly controls his believers and which is usually religious in tone - in which case not, or the new definition "a person or thing that is popular or fashionable among a particular group or section of society".
Under the new definition the Cass report suggests that yes, it may well be a cult in this sense. Cass mentions that 15 years ago only 50 people, predominantly birth registered boys were being seen by gender identity services, but today there are more than 3000, many of which were birth registered girls presenting in early teens often with quite complex additional problems. Couple that with the tendency for "in trends" from social media and it lends weight to the idea that there is a cult element to the current wave of gender identity referrals.
This needs care, I might say caution. Trends not are not limited to attraction. In the case of the rise in the number of biological girls looking to transition may not only be cases of attraction to be the thing, but an escape from the opposite thing. In other words girls may be wishing to escape from being girls; and within a system promoted as binary, this gives the choices of boy or non-binary.
I agree with Cass concerning social media, as I have said before. The HopeNotHate report shows that misogyny among boys/young men is on the increase reportedly from influencers such as Andrew Tate. Who can blame girls for looking from an escape from this kind of bigotry?
This is why I have cautioned about the assumption that these girls are gay rather than trans. It is not the only explanation, and it is unscientific to assume that it is.
If hate speech could be brought to an end, and the numbers of trans referral cases diminished, that would be an indicator (but not a proof).
The ideology of absolute free speech free from consequence is a dangerous one. Some will argue that free speech is not gradable. I will argue that it already is, but the bar is set so high, that hate speech can not easily be legally challenged.
If we fail to notice that hate speech is harming children, continue to advocate for absolute free speech, then we can not claim to be interested in defending and caring for children, when we hear from young people that hate speech is ruining their lives.