I'm not an attorney, and have a limited insight into the law. COVID-19 and the legal issues around employment have only begun to take form. These ideas are all just something that comes to mind, off a quick search. Only a practicing attorney, and preferably, a litigating attorney (someone who argues cases in court) would be able to give you solid advice.
My first thoughts:
You could attempt to pursue legal action, yes, but it would be most likely an argument based on breach-of-contract, or, a complaint of immediate threat to your health and safety.
There is past reference that could indicate you can reasonably argue that imminent harm, is enough to justify based on a perceived threat of injury that has not yet come to pass. The threat / harm would need to be proved as 'certain / likely / impending' to cause injury, in a factual way. Mere allegations of possible future injury are not sufficient generally not sufficient.
It would be possible to prove that this is a situation. But, I'm not sure.
Local governments, namely those that are county bodies - in the DFW area, have all issued declarations of emergency, asserting their authority under the Disaster Recovery Act of 1975, and Texas legal and provisional statutes. This means that there is a real situation that is recognized by the government, as a public emergency.
A number of lawsuits, based on a brief search of the LEXIS and WESTLAW database, show a variety of orders from the supreme court of Texas, and multiple federal district courts, related to the responsibilities balanced in the interest of the state, versus individuals.
Few, if any of these cases directly contain clear information about any school district employee - however, there are some suits that are in process that contain fundamental issues similar to yours.
It is unclear how a Civil Action would proceed. The basic process would likely be a notification of intent to sue, delivered to your District, and possibly, the University Interscholastic League.
The legal standing for an employee to bring action against both of these agencies, seems to be - as far as I can find - questionable. Regardless, you are a citizen, and resident of Texas, and entitled to the rights - with few exceptions - guaranteed in the US and Texas Constitution.
Meaning - you are entitled to your day in court. Whether or not you have the legal ability to sue these entities, is unclear - if you're doing so in your capacity as a teacher. A student or parent, however, would have much clearer room to sue.
All of this is based on you having done everything reasonably possible to get help and bring your concerns clearly and firmly to your direct supervisor (principal usually) and up the chain of command, including a letter or notice given to the Board of Trustees, and Superintendent.
You could make the argument in a few ways, through a few different avenues. None of these are preferable, as legal actions are difficult, and most civil cases do not reach a verdict.
1. An emergency request for an injunction and temporary / permanent restraining order, in a court (likely a district court, or state court) that would be based on the contents of both your county's local declaration of a disaster, advisories put out by the state department of health and human services, your county health department, and the Centers for Disease Control, along with the US Department of Education.
You would essentially be arguing that in being forced to participate in 'non-essential' activity, a clear and immediate danger or threat to your health is put at risk that is so grave, and serious, that if you've tried to take all available courses of action to protect yourself, and been denied - meaning, your administration, FA director, and Board / Superintendent, have been made aware of your concerns, you are asking the court to order the district and / or UIL to suspend these activities. This would be difficult to prove, but not impossible. It could put your employment at risk in the future.
2. A Civil Action (lawsuit) against your employer (school district) alleging a hostile or unsafe workplace environment that forces yourself into a situation where you have no reasonable way to protect your health and safety. Here, you would be arguing a breach of contract - claiming that the district failed to uphold their obligation under your agreement / employment, to provide a safe, non-hostile, and reasonable workplace free from harm or threat to your health. This would be more difficult to prove, and would be a costly, protracted, time consuming ordeal. Your employment may be at risk, but, not entirely.
3. A lawsuit against a district, board of trustees, UIL, interested party or single party, based on a constitutional or procedural violation, which argues your rights are violated. You would need to argue and attempt to prove that requiring you to participate in these events is outside the normal boundary of 'reasonable' risk or behavior normally required by the duties of employees in general, violates your rights. This would be very difficult to prove.
It is election season - and many folks are up for election on the boards of education. It would be possible to contact your school board trustees about your concerns.
They have the ultimate responsibility for the safety of the teachers in the district. They are also the group that is usually sued, and have to defend the allegations in lawsuits, through the school district's legal team.
They have insurance for this, but generally, try to avoid any litigation if possible. My recommendation would be to consult a workplace or employment attorney, that specializes in these things, but, it's very possible the board of trustees would be willing to listen to your complaints, and, if you can get the boosters or community leaders / organizations to back you, or even speak on your behalf to the board of trustees, they might be able to internally help you out.
Good luck. : - (