Well, if you were eating it with a fork anyway the I don't see the problem... A lot of Mexican places (as opposed to Tex Mex) will also pou salsa or queso or something over the burrito, which then obviously requires a fork, but it's also different from the burrito pictured.

And you know you can just ask them not to put any cilantro on? It's a garnish that typically isn't added until the very end and a lot of people can't stand the stuff, they probably won't mind leaving it off