I’m Latino (Venezuela) and I have been to the Philipines. In general, Latinos and Filipinos don’t look alike but many—millions—do, because the original indigenous Americans, from Alaska to Patagonia, are of Asian (Siberian and Polynesian) origin. And Filipinos are a wild mix of Asian, Polynesian, with some European (Spanish) and even some with African (the Aetas). If you look at the indigenous tribes of the Amazon, of the highlands of Peru and Bolivia, of the Southwestern United States, of Northwestern Canada, they look like many Filipinos. Many Filipinos actually look less Asian than many Amazonian indigenous people. Visiting the Philipines, I was surprised at how many Filipinos look like many Latin Americans from Peru to the Caribbean. The Filipinos of Aeta origin look like any Latin American from the coastal cacao-growing towns along the Caribbean. The Lumad, Badjaos, Igorot, etc. also look like some Latin American indigenous groups.
Anyway, the average Filipino looks more Southeast Asian while the average Latin American does not. But even though you could perfectly differentiate a group of 100 random Filipinos from a group of 100 random Venezuelans/Colombians, you will find some that are similar. Look at the current and former Miss Philippines. Their faces are like those of millions that you’ll find in Colombia/Venezuela. You put those girls in a Venezuelan/Colombian gym working out and nobody will ever think that they are not local girls.
And here are Philipinos of Aeta origin. There are millions of Latinos that look like them too (Would you guess they are Filipinos?).
Conclusion: Average Filipinos (not Miss Universes and not a remote tribe), have high Southeast Asian DNA (China, Malaysia, Polynesia) while Latin Americans have high indigenous (Native American) and European DNA (Spain, Italy, Portugal). So I can’t say we “look alike” but many—millions of us—do. Anyway, look like us or not, Filipinos are part of the Hispanic world from the Iberian point of view (Spanish colonial origin). They are our Asian cousins.