Kathoey are not LGBTQ. The word glosses better as intersex, and that's how they are seen. You cant choose to become or come out as, a kathoei...
Regarding them as transgender, or gay, is cultural appropriation.
People who appropriate 'third sex' categories, for things like gender identities, ought to remember the historical use of a 'thrd sex' ie. a eunuch or neuter, physically ambiguous and defaulting to effeminacy.
Kathoei are only aware of it in middle childhood, unlike current Western narratives that have 3 to 5 year olds profess a trans identity. Earlier in childhood, adults will be aware of kathoey tendencies in the male child: play behavior, and body language, and the like.
Naturally self-awareness intensifies during puberty, although they dont develop macho frames or muscle mass. No one claims them, literally, to be natal women with penises. Just that they are biologically 'off' as men. This is the point of commonality with Western transsexuals, but only with the early onset subset.