If you lied on your employment record or omitted convictions yes you can be terminated.
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As an at will employee, you can be fired anytime for any reason that is not unlawful. The employer is not required to state the reason for termination, nor is the employer required to be truthful or complete in any voluntary statement about the reasons. So, necessarily, yes, you can be fired for having a criminal record. Or for having a $5 bill in your pocket. Or ANY other reason that is not specifically unlawful.
If you are terminated based on your criminal history as that is revealed by an examination of your specific history, then by definition you have not been excluded from employment by a blanket policy that may be within the EEOC's ambivalent and nebulously-stated position on this issue.
If you are asked, disclose. If you disclose, be truthful. You do not control the employer's decision-making in this situation.
The employer can, of course, voluntarily waive or hold in abeyance any implementation of its policies on the issue of criminal record history as a factor.
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As an at will employee, you can legally be terminated for nearly anything, even something as silly as you happen to be one of two people walking by right after a boss reads an email directing him to eliminate two positions from the department. Not all bosses make the best decisions.
Long and short of it, it's probably a good idea to start working on the search for new employment.