No they don’t and for a reason.
They don’t believe identity is malleable in any way but hereditical.
True, their meme would be far more accurate if it portrayed someone like Rachel Dozel, as they believe that people mostly transition for personal gain rather than personal preference.
I believe they’ve made a meme to that effect before.
Where it all falls apart in the comparison is that there are genuine interracial people and intersex people. These people tend to overlook those people who come from two identities. Their oversimplified morales might prefer that their father strictly dictate their identities in terms of race but they would rather anyone born with a phallis of any kind, functioning or not, be identified as male. And those without, even eunuchs misidentified at birth, be identified as female. Ideally, race nor gender would strictly determine one’s identity but both sides of this argument are too hardcoded by “tradition” to do so.
One could argue that transpeople tend to take such identity to an extreme but when the only side that would even consider arguing that would rather send them to a re-education/brainwashing camp for the ones they can groom to their “traditional” lifestyle… and continuing to create discriminatory laws for the rest of them, it tends to make any attempt to argue that there is a line where transpeople “go too far” pointless.