Most people who commission an exterior or public-facing mural assume that it needs an anti-graffiti varnish. Not at all. Mural art deters tagging and graffiti. Murals rarely get tagged because of a culture of respect for the work of other artists among street artists—and also because, in general, taggers would prefer to have a blank wall all to themselves. The paints I suggest are durable; accidental or incidental marks from crayon to sharpie can be removed with warm soapy water or a mild degreaser. Varnish is expensive and significantly increases the total cost of a project in materials and labor hours to apply it. On projects with a tight budget, I think it is better to put the money towards better artwork than protecting a low-budget piece with varnish. Unvarnished murals also are easier to touch up, since the artist can just walk up and paint on the wall without first having to remove the protective varnish. The only thing more toxic than varnish is varnish remover.
There are two situations in which I recommend varnishing a mural. The first is if a mural is painted on a public wall that has been a long-time target of tagging and graffiti. A good anti-graffiti varnish that I would recommend in this situation is TSW (This Stuff Works) made by Graffiti Masters. For a public mural, the client (building owner, city, or school district) should be in charge of purchasing and applying the graffiti varnish, since they are the most invested in the long-term maintenance of the mural.
The second situation in which I recommend a varnish is on walls that receive more than eight hours a day of full sun exposure. In this case, I recommend a UV varnish. I use a product made by Marabu, called Clear Shield, in the matte finish. (It looks more like an eggshell finish.) (Some anti-graffiti varnishes offer UV protection, but most UV varnishes are not categorized as graffiti-resistant.)
When I paint murals on south- and west-facing walls, I exaggerate the warm tones during the painting process to anticipate a bit of fading, and then apply extra coats of the UV varnish over the warm-colored areas of the mural (red, orange, yellow), as those colors are most vulnerable to UV rays. Murals with south-facing sun exposure should have a UV varnish reapplied every five years or so. East- and west-facing murals should have a UV varnish re-applied about every 10 years. North-facing walls do not need a UV varnish.