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Gluten free food in Mexico
Eating gluten free in Mexico is fairly easy, diet is basically corn based (more so in the central-south than in the north). Corn tortillas are the norm in the central-south and in the north you will usually have an option to both, though "burritos" will always be in flour tortillas
"Safe" food in restaurants
All salsas, including guacamole will be made from scratch (so far never encountered one that made me sick, be it on the street stalls or in the restaurants)
All tacos (except fish or seafood) will be made from plain meat on the grill (usually steak)
Machaca (north)
Cochinita Pibil (Yucatan)
Veracruz style fish fillet (Veracruz!)
Any filling used in quesadillas (the ones from Mexico City which are hand made on the spot) (chicken tinga, mushrooms, pumpkin flower, cheese, chicarron, tinga de res, etc)
Soups (except fideo, which is pasta and sometimes vegetable soup or Juliana soup which is a vegetable soup but with noodles in it) safer bets are sopa de tortilla, consome de pollo (this one has rice in it), caldo talpegno and Pozole (main dish)
Any type of "barbacoa" will be a safe bet, the style ranges from state to state, but it is usually lamb meat with spices
Pipian (peanut based sauce, can be done with either pumpkin seeds or peanuts)
Steak is readily available in all restaurants, the easiest dish is a "Tampiquegna" which is a steak with guacamole and a small enchilada (make sure it is not a mole enchilada, it is usually either green sauce or red sauce both of which are fine) and beans as well
Pescado empapelado (fish steamed inside paper)
Chicken fillets are available in most places, just make sure it is not breaded (i.e. "enpanizado")
All mains in a sauce should be safe, sauces in Mexico tend to be watery clear, not milky thick (except mole and nogada, though nogada is safe) so do not fear to try puntas de filete en chile pasilla or pechuga de pollo en salsa de mango or anything in some "salsa", stay clear of anything that is not local, like "bechamel" sauce, this one will probably not be gluten free or tartar sauce either.
Shrimp tend to be not battered, safe bets are "al mojo de ajo" and "a la diabla" (hot)
Foods to avoid
Mole (sorry!)
Chiles rellenos (battered)
Fish and seafood tacos (battered)
Milanezas (breaded steak or chicken fillet that is later fried)
Quesadillas from a "restaurant" that is NOT a taqueria where they are being made from corn flour (quesadillas in the north are just flour tortillas with cheese, while in Mexico City they are oval shaped corn tortillas that are filled with an assortment of dishes) (see above)
If you are in Baja, stay clear of the "Agua de Cebada" (Barley water) this is usually sold at the fish taco stands and is similar to Horchata, but while Horchata is rice based, barley-water is... you guessed it! Barley based (looks browner than Horchata)
On a shoestring
any market will have fresh food and vegetables
Rotisserie chicken is readily available and they usually supply the corn tortillas and the salsa as well
Tamales (most are available at 6am or so) along with a calorie packed atole
Fruit stands (if your intestinal flora can cope with it) they also have some chopped veggies here like beetroot, carrots and jicama
Street tacos
Eat at fondas, the ladies there prepare the food daily on the spot and will know exactly what went into it, most fonda menus include a "pasta" soup at the start, just avoid that course and the rest will most likely be ok
Snacks and trekking munchies
Chocolate covered raisins and almonds from Ricolino are available in practially any little shop in Mexico (look for an acrylic boxy display case on top of the counter)
Snickers and Milky Way are available as well
Assorted chocolates
Dried fruit and seeds are a bit too dry for my taste and not very cheap either, can be bought at some markets and at the supermarkets
Alegrias, plain or chocolate covered are a fabulous treat, not readily available in the North unless you go to a health food store and even then they will not be as nice as the "fresh" ones.
Health food stores have sesame seed bars and some have pecan and almond bars stuck with sugar
Sweets
Try the artisanal type, those will all be GF
Mazapan (sold in any shop) is powdered peanut with sugar and a hint of cinammon, commercially made and readily available (I have tried La Rosa and El Cerezo brands and both have proven safe)
Dulce de coco or cocada, coconut candy one has milk the other one does not
Cajeta! Something similar to a runny toffee, it is usually served over bread but in the area of Celaya (Guanajuato and other abundant dairy producing areas) it is abundantly produced and sold in tiny wood tubs for personal consumption with a spoon
Ate de Membrillo or Ate de Guayaba, also more available in the orchard-rich areas of Michoacan and Guanajuato, it is fruit boiled down to a sort of jam but it solidifies, usually served with a slice of cheese if available at a restaurant
Alegrias (made from amaranth, very nutritious) (see trekking munchies)
Palanquetas or pipitorias or pepitorias, the Mexican equivalent of peanut brittle
Tamarind candy (pits included) all come sweetened with sugar and some will have chilli as well, you can get them with lemon juice at the markets at times
Popsicles (from la Michoacana, there is one in every street corner) sorbets will also be safe, ice cream is getting way too processed now so I would stay clear of it unless it states it is made from 100% cream (Santa Clara will be a safe bet)
Raspados (shaved ice with fruit syrups) (available anywhere is Summer)
Candied/crystallized fruits, available less and less now but you can get them at the markets and at some traditional candy stores in the small towns, usually sold by street vendors with baskets (lemons stuffed with coconut, figs, candied pumpkin, crystallized oranges, etc.)
Hope if you are a celiac and wanted to visit Mexico, the wide array of available food has tempted you more!
BTW, tequila is GF ;-)