The "sort of" refers to how they were both Spanish colonies, ruled from Mexico City as the Viceroyalty of New Spain.
In the Philippines:
In Mexico:
While one can say that the Philippines has a different cultural attitude to these issues which is incomparable to Western nations or Mexico (for example, the phenomenon of Bakla), is there a reason why the legislation in the Philippines has remained far more steadfast to Catholic teachings than that of Mexico? Both Mexico and the Philippines have indigenous peoples converted to Catholicism by the Spanish, and later were heavily influenced by the USA.
From my own experience, it seems like left vs right politics is still nascent in the Philippines, it's still mainly personality-based politics there.
You are frankly making an apples and oranges comparison based on a flawed premise. As you acknowledge yourself, Filipino and Mexican culture did not start with Spain or Catholicism. But instead involved the imposition of new mores onto extent cultures.
This is not like asking “why might Anglo-Canadians and English people disagree on X issue”. It is an entirely different anthropological kind of question about cross-cultural comparison, instead of about divergence from the point t0.
I think the most important point to emphasize in this regard is that Mexico was a settler colony, with Iberians physically bringing their norms and institutions with them as they emigrated (in addition to their genes).
The Philippines was not a product of any similar process of métissage. Spanish and later American institutions were laid on top of existing Filipino institutions in an essentially extractive manner, characteristic of European colonialism in Asia and Africa.
This is all to say that the contrasts you draw between the Philippines and Mexico may have very little to do with their shared experience of Catholicism, and instead from other institutional arrangements, preexisting cultural mores, etc.
You give an example of this yourself when you mention Bakla in the Philippines. LGBT people don’t have constitutional legal protections because both of those things- the concept of LGBT and liberal ideas of individual rights- are foreign to Southeast Asia. Bakla and their equivalents across SEA (katheouy in Cambodia and Thailand, waria in Indonesia, etc.) are not “LGBT”, they are just a gender category which already exists in the schema of the SEAsian world. Applying the label “queer” is a(n ahistorical) western innovation, and the idea that they would need constitutional protections seems odd, because they are not minoritized in the same way (although they certainly do face discrimination and have faced discrimination historically).
Thus the puzzle is not, “why has the Philippines stayed so conservative, while Mexico is not”. This presumes that there was a similar starting point which never existed, especially across such a long time period and a polity so diverse as the Spanish empire.
E: if you’re interested specifically in the question of growing liberal attitudes in Mexico on these questions, there’s great work in Political Science on the “justice cascade” that followed the third wave of democratization in the 1990s. Feminist and queer issues are viewed very progressively across parts of Latin America, in large part because of the work of transnational linkages between activists, which emerged out of the democracy movements in the Southern Cone in the 1980s