‘This Catholic contingent is member of what would be considered a “renegade” chapel in San Antonio that belongs to the Society of St. Pius X (SSPX). The SSPX is considered to be in a “schismatic” status since they adhere to the Traditional Rite of the Catholic Mass that was celebrated before the changes of the Second Vatican Council.’
Since the Church allows the Traditional Rite to be celebrated in accordance with Ecclesia Dei, the adherence to the "Traditional Rite" is obviously NOT the reason why the SSPX is in schism.
I don’t see how he can deny them admission to the Mission, particularly if it’s run by the Park Service. This is a very strange story. I don’t know anything about Gomez, but it would be interesting to learn more from anybody who knows.