I live in Texas. Our labor laws are some of the worst. However, even here I think a blanket clause from a startup that prohibits outside employment sounds fishy. Researching this I found the Texas Guidebook for Employees which has this to say in Conflict of Interest,
It is generally inadvisable to flatly prohibit all outside employment. Many people work two or three jobs. The real concern should be with outside work that interferes with the employee's ability to be a good employee for the employer. For example, an employer may legally prohibit any outside work for a competitor of the company; that conflicts with the working hours for the company; that undercuts the company's image, mission, or goals; or that makes the employee so tired that the employee cannot function effectively in the job he or she performs for the company.
That's not very good guidance though. When it says it's "generally inadvisable", what's the reading of that? Does that mean the court will enforce it if it is written that way, and that this Guidebook amounts to mere morality training for employeers?