Yes, you've got the basic idea. The transphobes like to tell this narrative: Once upon a time, only a very few people were psychiatrically diagnosed as "transsexuals" according to specific criteria, got approved for hormones and surgeries, and their transition was supposed to be completely binary (man to woman, or woman to man), following whatever rules. Now the idea has been broadened to "transgender," which includes people who aren't following the "old rules," may not want any hormones/surgery at all, may not be looking for a therapist's permission for anything, may be openly trans (gasp) rather than keeping their pre-transition history secret, may use "they" pronouns or live in more than one gender at different times, etc. In the transphobes' narrative, the old-style "transsexuals" might have been allowable/forgivable because they sought official permission from the system and weren't highly visible. But today, trans people are under a very large umbrella, no one knows where the boundaries of anything are anymore, cis people can't control trans people's behavior, there are too many trans people, they are taking over the world, etc. And when the transphobes put an "-ism" on the end of it (transsexualism and transgenderism), they mean to imply that there's some "ideology," which could be an ideology of physicians and academics or else a political agenda held by trans people ourselves, but in any case is an ideology that the transphobes consider bad. They never explain what this ideology is — they can't, because it does not exist.