I don’t think political affiliation is considered a protected class for commercial non-discrimination.
That would be for the court to decide. Per Wikipedia:
Discrimination is the prejudicial and/or distinguishing treatment of an individual based on their actual or perceived membership in a certain group or category, such as their race, gender, sexual orientation, gender identity, national origin, color, ethnicity, religion, language, disability, age, socioeconomic status, or other characteristics.
That potentially includes everything. But, as I said, merits of the case are irrelevant if they use the lawsuit as a PR stunt or as a threat. For example, they can demand a settlement that puts the gun store out of business; gun stores are not casinos, they don't swim in cash. The owner had a duty to protect his business and his employees, and, IMO, he fulfilled that duty in the safest way possible.