The question you raised is harder than you may imagine.
Nationwide, state and federal courts have ruled that in some matters, religious organizations can make their own rules about employees that would be illegal if the employer was not part of a church or religious organization. For example, a church may decide that it will only hire people of its own faith. Or a particular organization may employ only men. Or a church may require employees to engage or not engage in certain type of behavior - for example, it may be legally all right for a church to fire an employee who has an abortion.
I can think of policy reasons regarding why a church/religious organization may have the rule you mention for their missionaries. Whether or not this type of rule has been litigated would take quite a bit of legal research. It's not something I can answer off the top of my head.
You asked me to cite laws - the starting place for legal research would, of course, be the First Amendment to the US Constitution. That's the starting point for looking at whether there are ANY limits at all on what rules a church can make for its employees (on the theory that a missionary is a type of employee, even if a volunteer, and even if paying for the privilege of being a missionary).
If you would like detailed legal research, I will have to opt out and perhaps someone else will be willing to do the research.
Please feel free to write back, or click "accept" if I have answered your question.