In those cases where my employers have made "No discussions of politics or religion" a condition of my continued employment, I have followed the rule, but only while on paid company time (that is, while I'm "on the clock") or on company property (that is, property that is owned by the company).
This means that even if I attend a company function - a retirement luncheon, for example - in a restaurant, I can legally discuss politics and religion without fear of legal reprisal.
However, in the example that you cite, it seems to me that the policy is stated only to keep the company from getting sued for religious or political harassment, and not any of its employees.
This way, if a coworker who believes (or dis-believes) in a particular candidate or deity starts trying to convert you while at work, the company can legally disavow any approval (expressed, implied, tacit, or otherwise) of your coworker's actions.
Advice (take it or leave it):
1) Update your résumé.
2) Remove all of your signs and symbols of your beliefs from your workplace.
3) Post a photocopy of your company's anti-religion / anti-politics policy where everyone can see it (highlight the relevant statements).
4) Obliquely and privately remind the offending party of company policy.
5) Be prepared for backlash.
I am sorry to say that there are fundies who believe that they are above secular rules, and that they are free to flout them at will. You will find that these people are either exceptionally valuable to the company, or that their chances for promotion and/or continued employment is about to end.