It is always hard to understand another country’s context.
en.m.wikipedia.org/wiki/Rodrigo_Duterte
Like him or loathe him, Duterte’s election possibly results from his strong (!!!) line on drugs. I don’t know about the Philippines but transgenderism, of the ‘ladyboy’ type is a familiar and long established phenomenon in South and SouthEast Asia. Different from Western AGPs perhaps, more akin to an extreme campness.
The SE Asian language I speak, not Tagalog, does not seem distinguish between ladyboy and gay. But perhaps it was a conversation that I never really had. Ladyboys existed and were effectively accepted for what they were, which was not women but a sort of third sex. And indeed I was aware of a transgender FtoM who was equally accepted within her family and passed as a man to outsiders. Homosexuality was culturally not accepted. It clearly existed but was not discussed. A friend had a gay BiL who lived in the UK and used to bring his long term partner with him on visits. Neither she nor her BiL explained the details to the PiLs and they did not seem to suspect that there was anything beyond friendship, though she wondered at their apparent naivety. She,, although an educated English speaking professional, clearly tolerated rather than approved.
The UK as a Western Anglophone country has problems with the US pushing their cultural norms on us. The same is true, albeit more so, in Asia.
FWIW Taiwan has a transgender Cabinet Minister, previously a high flying computer expert.