Historically, a fire department is empowered withe what is known as "plenary authority" to carry out its function in protecting the public. This authority is practically impervious to challenge, as long as the fire department personnel are acting within their scope of duties. In your question you state that there was in fact a fire at the end of your private road, so the department is acting within its authority, as long as it takes reasonable steps to reopen the road to the residents when the fire danger has passed.
Obviously, there is some gray area in this scope of authority. By example, the U.S. Supreme Court has ruled that the police cannot hold a driver at a trafficc stop while waiting for a drug sniffing dog to arrive, if the original reason for the traffic stop has been completed (driver cited for traffic offense -- no obvious sign of drug use). See Rodriguez v. United States,***** 1609 (2015). Extending the example to the fire department, if the fire department were to continue to block the road after it had determined that there was no danger of a flare up, then blocking the road would likely be considered a public taking in violation of the due process clause of the 5th Amendment -- or, perhaps even an unlawful arrest of the property owners residing along the road.
As you can see, the gray area is what creates the dispute. And, sometimes, the dispute ends up in the U.S. Supreme Court. This is the sort of situation where people contact the ACLU and request assistance -- because the ACLU is in the business of protecting people's civil rights when allegedly infringed by the government. So, if you want to take the matter further, you may want to contract the Texas ACLU branch.
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