People without food allergies often don't know what's involved in making sure something is truly allergen-free. While there are some prepackaged food manufacturers who guarantee the absence of allergens from their products, such as Enjoy Life Foods, most packaged products have minimal information, if any.
While some people with food allergies opt to only consume fresh food they know is safe, requiring either minimal preparation or prepared in a safe environment, that's often not an option, especially while traveling. Each person has to decide for themself what they require in order to feel safe with a food product.
Allergens can be introduced directly (as an ingredient), indirectly (through the use of shared equipment to create or process the product), environmentally (used in the same facility but not on the same equipment), or via third-party contamination of individual ingredients.
Most products, especially from big-name brands, will list the allergens in a product on the label, but they won't necessarily list whether the product is processed on shared equipment that may be contaminated, or in a shared facility, or if their ingredients are guaranteed allergen-free.
If the label's information is incomplete (which it almost always is), it can help to search the web for "product name allergen info" and see if anything jumps out. Often, there will be posts on forums from other people who've done the necessary research on a particular product, and then you have to decide if you trust their research based on nebulous factors like how thorough they seem to be and how old the information is. (Some products were safe at one point but have changed since then, and there's often no way to tell.)
If there's no good information like that, then you can either email (if there's time to wait for a response) or call the company directly. Most of the time, unless the company is particularly aware of allergy issues, or it's a small company, you'll get a vague answer like "we clearly indicate allergen information the packaging but we cannot guarantee safety", designed explicitly to give the company legal protection and not actually be helpful. It's a judgment call. Larger companies are more likely to have entire dedicated prodction and processing facilities for individual products, so cross-contamination is less likely.
Sometimes, though, they'll be aware of all this, and will tell you that it's processed on its own line (meaning no indirect contamination), or in its own facility (meaning no environmental contamination), or in a shared facility but the other products contain no eggs or nuts, etc. If the company knows enough about allergy safety to be able to answer in this way, it's usually a safe bet that they have a good handle on allergen safety. Hardly anyone guarantees their third-party ingredients. It's safest to ask specifically about the line, the facility, and the ingredients if they don't volunteer the information. Most of the time, they end up saying they don't actually know and fall back to "we can't guarantee it," which, again, leaves the decision up in the air.