Actually, my question is not whether you can refuse to notarize a document once you are a notary, but, can your employer require you to become a notary as a responsibility of the position? I have always understood that they could not since it is not a matter of employer liability but the employees personal liability.
If you are notarizing documents of behalf of your employer, it's my understanding that the employer has the liability with the liability covered under the employers errors and omissions policy.
You do bring up an interesting point, e.g. if a notary cannot refuse to notarize a document, in this case a non-employer related document, that notary would have liability that would not be covered by the employer. Therefore, it seems to me that an employer cannot force someone to be a notary as the liability may extend to non-employer notary tasks. On the other hand, if notary services are required as part of the job, it appears that an employer can decline to hire someone that will not become a notary.