I see. I certainly understand your hesitation in complying with such a demand as your reputation may be on the line.
State law typically does protect employees from retaliation who refuse to engage in unlawful conduct and a clear breach of contract would arguably involve unlawful conduct.
However, you would need proof that the demand is being made of you, so it is important to gather an preserve any such evidence, so that if the employer does retaliate, you can prove your case for lost wages and benefits.
If you wish to prevent retaliation altogether, it would be best to retain a local employment law attorney to communicate with the employer on your behalf, informing them of your legal rights and attempting to resolve the situation without having to resort to legal action, as that would not be anyone's best interests if it can be avoided.
Here is a link that summarizes state law on this issue:
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