When a company forces you to sign a form, can you be fired for adding " signed under protest" with your signature?

The answer to your question is more complicated than you might think, and I really don't have enough information in your question to provide more than a general response.  To begin with "signing under protest" really has no effect; it simply says the employee disagrees with signing the form.  From what you describe, there is a procedure for disposing of oil product and contaminated rags which involves 2 separate locals.  These materials have to be disposed of properly or the employer can face possible violations of environmental laws.  I suspect the employer has therefore put a specific procedure in place which complies with legal and contractual requirements, and any deviation from that procedure may result in either EPA citations or grievances under the labor agreements.  As part of the process, the company insists the employees sign the form.  An employee "signing under protest" can have implications for the company in the sense that the "restriction" on the signature could be interpreted as an indication the person signing the form either didn't follow the required procedure, or is somehow challenging the procedure.  Under those circumstances, the company has decided it is necessary to take disciplinary action against employees who seek to restrict their compliance.