Highly improper and wrongful under both state and federal laws. And I am certain that your local Republican party group would not be pleased to hear about this either, as any lawsuit would likely call press coverage to the dispute. Contact a good employment lawyer who is in your area to discuss how to strategically handle this matter in a professional yet respectful manner.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.
Whether your employer's instructions and the assignment to place the signs was unlawful or improper depends on the nature of your employment. There are certainly many kinds of employment for which that work assignment would raise no legal issues. If the work assignment itself is not improper, your termination was not unlawful because you were an at will employee and at will employees can be terminated for almost any reason (the exceptions are not raised by anything of your factual recitals in your post). If for some reason the assignment itself was improper, then very likely the termination was unlawful.
The important distinction here is that, based on what you have written, you were not terminated for not being Republican or any other "political" reason. You were terminated for refusing for personal reasons to do a specific task and/or for a defiant and hostile attitude and statement when your employer pressed you to complete the task as assigned. In at will employment, terminations on such facts are not unlawful. Based on your post, it seems that you conflated installing the signs with "campaigning." But, if you think about it, there is a substantial and powerful difference. The installers of billboards don't get to refuse assignments because they don't like the advertised product.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.