I'm assuming you're talking about their corn chips (all I've ever run across from Mission). As long as the chips are 'plain' there shouldn't be any problem with them. Just be very careful about flavored chips since that's where the non-veg ingredients come into play with corn chips (I've got no idea if they make flavored corn chips).
As a general rule the processing of corn tortillas is on dedicated equipment and there's not much chance of cross-contamination in that part of production.
The same goes for fryers used to make corn chips from the tortillas (*unless* mission also makes pork rinds). If they make flavored chips in addition to unflavored that would normally be the point where animal ingredients would be involved since dairy and other animal 'stuff' is frequently used in the production and application of flavorings. That would be the most likely point of cross-contamination, but from experience production lines get a *massive* clean-up between production runs.
Keep in mind that with nationwide companies production isn't usually confined to one production plant, they'll have several and may even lease space on other companies production lines. You've got to check with the company for details, asking them this question can help since it's a legally binding question:
"Does your product contain any animal ingredients, or any ingredients processed with animal products, or any ingredients that originally derived from an animal source and/or are any products originally from an animal source used in the manufacture of your product?"
I don't have any link that detail the production practices of Mission (or any other tortilla/chip maker for that matter). My knowledge has been obtained from the years I spent taking care of industrial process control systems.