Butter and lard were semisolid fats used long before margarine or shortening were invented and should work just fine.

Personally, I'd go for butter, although the texture might be a little off. And the flavor might not be "authentic". Margarine is even less healthy than the hydrogenated oil called shortening-- it's nasty stuff, but can be used in a pinch if there's some lying around.

Good lard, "leaf lard", is tough to find and most of what you see in the supermarket is lard mixed with shortening. And pig fat doesn't seem to be close to authentic Indian, although it will work.

Just take about 4-6 strips of bacon, cut them into 1" pieces with kitchen sheers, and put them in a medium sauce pan over medium heat. Immediately add 3 tbs of water before the pan heats up. The water will help render out the fat. Once the water evaporates, skim off 2 tbs of fat into a small cup. Finish cooking the bacon and save it for a blt or salad. When the fat cools the lard will be on top and any left over liquid will be on the bottom.

there are lots of vegetarian/vegan options:

I substitute canola oil for butter or shortening all the time.\ when making breads. Also when the bread recipe calls for such a small amount of fat in relation to the amount of flour, you could just leave the shortening or fat out entirely. I always leave out the fat when I make cornbread. Can't tell the difference. If there was a difference , it would be a crisper bread and since you are going to make a fry bread, the lack of fat in the recipe would not be noticeable.

I also turn it around. I like to use a Betty Crocker white cake mix when I make an Italian cream cake, The box instructions call for oil, but I use softened butter instead.

you can buy 1 lb blocks of lard or shortening and it keeps forever (use it up in pie crusts )

OMFG fry bread! you are evil!

Shortening is a very pure fat, so it will keep for a very long time.

If you want to go purely 'authentic', lard is the proper way.

Look on line for the history of frybread, if you want an interesting 'voyage'.

...just like cubes of butter in size. Crisco changed its formulation some recent years ago to something more healthy. Many cooks don't like the new stuff because it handles differently when making pastry. But an occasional bit of it won't hurt you.

Kroger sells house brand of shortening that works like the old crisco. Yes, it's hydrogenated. But how often do we eat pie, anyway?

I went looking for a photo of it with refried beans, shredded cheese, shredded lettuce, and guacamole, and stumbled across this shortening-less recipe:

http://www.livingonadime.com/recipes/navajo-tacos.html

One of my 'redeeming vices'. Every time I go by the Historic Trading Post at Cameron, AZ I have to stop off for one. It looks a lot like your picture, but there is a nice meaty chili between the frybread and the lettuce. The restaraunt is run by members of the Nation and completely staffed by them also. If you're ever in the neighborhood, it's a must stop place.