Is this illegal under equal employment?

this is discrimination, it could be covered by religious, national origin, and/or race......

http://www.eeoc.gov/employees/

The EEOC is very clear about this. Basically, religion legally can't be made part of why someone is hired, fired, promoted, demoted or in any other way considered in any aspect of their employment. So even if it was something that an employer required every employee to do (not just certain faiths) that required all employees to disclose their religion, it would be illegal.

The EEOC also has very clear directions on how to file a charge.

Are all employees required to take this oath, regardless of what religion they are?

EDIT: Okay, if it's only the Muslim employees who are required to take this "loyalty oath", then yes, I would say you have a VERY viable case. However, I am not a lawyer. You should consult somebody who is.

in the USA yes so long as the employer does not have federal contracts most other countries no

Yes, that is definitely considered discrimination.

yes,