While Mexican law doesn't have any real requirements regarding language, culture or ethnicity, to most of the world, including Mexicans and non-Mexicans, these three points define being Mexican, entirely. So, how Mexican am I, really? Let's consider the three points.
Language. I speak Spanish half decently. I have an unmistakable foreign accent, but I've got passed the point where everyone automatically assumes I'm a gringo. I've had people ask if I'm French, German, and, even once - bless this person! - Spanish (they could tell I sounded funny, but couldn't put their finger on exactly what it was.) Of course, needless to say, most people still assume Gringo, and I've got a ways to go before this one counts in my favour.
Culture. Mexican culture includes music, food, clothes, hairstyles, ways of interacting, concepts of personal space, and many other distinct features. Let's see - I listen to some Mexican music, but I'd like to become more familiar with it. I have Mexican food down; my wife is Mexican, and she complains that I make her eat to much mole. I also eat spicier food than she does, and I know how to make a number of Mexican dishes, more or less authentically.
I loose a lot of ground in clothes, hairstyle, ways of interacting and personal space. Although people aren't consciously aware of it, I believe these factors are actually as important as language and accent. My wife sees people in the street, and says, "That girl is from Mexico City," without hearing them speak. Their clothes, movements, and, I believe, even facial expressions are strong indicators. While Americans and northern Europeans look the same, as far as "racial" features are concerned, they don't look the same in terms of clothes, movements or even expressions. I think many people from countries with a well defined culture can sometimes identify their compatriots before hearing them speak. The only fool-proof method I've found for Canada is the MEC bags (Mountain Equipment Co-op), but this only works for younger, back-packer-type travellers. I've also found that more Canadians travel alone or in couples; but this is a huge generalization. I don't think I can recognize facial expressions.
Ethnicity. Specifically, the "Common ancestry" part of ethnicity, which more generally also includes the points above. Mexico has no official ethnicity policy, as far as I am aware of (as opposed to what I've heard about some European countries, that apparently make citizenship easier for people who can prove ancestry from that nationality.) But the most common ethnicity is Mestizo, or mixed between the Spanish colonists and various native peoples, and this is the ethnicity most people identify as "Mexican." A very small portion of the populations (less than personal claims) is purely one or the other. Strangely enough, I've known people who are very obviously of mostly native ancestry, but claim, very adamantly, that they are "Spanish." Some of them are about as Spanish as I am Chinese, ethnically speaking. By these terms, I'm just entirely left out of the picture.
Unknown to most people, Mexicans included, is that Mexico is actually is more of ethnic blend than this simple combination. There have been waves of immigrants from places like Bohemia and Lebanon, leaving some distinct footprints in Mexican culture. Some people have told me that out in the villages of Sinaloa there are tall, blond people who descended from the central European immigrants. ("Tall" and "blond" are relative, however.) One of the favourite kinds of tacos, "Al Pastor" (click here to see see a post with a picture) was influenced by Lebonese kebabs.
What should work in my favor, though, is the fact that my ethnic background actually has a strong presence in Mexico these days; the Old Colony Mennonites, or "Mexican Mennonites" which they're often called just because of this fact. People in Mexico know who they are, and the cheese they make has gained considerable fame. They've been around here since the 20's now, so many of them would only have "Mexican" to claim as their nationality; ethnically, however, they and Mexicans don't make any connection to one another. Their situation is somewhat similar to that of many Jewish communities, with the exception that they have remained linguistically and economically distinct; while they speak a dialect of German (my "first" language, actually) and live in the country in fairly economically independent communities, all Jewish people I know here speak Spanish as their family language, have Spanish names, and live in the cities (in somewhat closed-off enclaves, mind you.)
Well, the bottom line is, if you have to sit around trying to prove to people that you really are somewhat Mexican, it's a pretty good sign that you aren't; true Mexicans don't have to prove it. It reminds me of something Jewish again; I once asked a Canadian Jew if he was "practicing." His reply was that he didn't need practice. Real Mexicans don't need practice and don't need evidence.
So, for now, I'll have to be happy with a passport, birth certificate and a voter's ID card.