When followers of a particular sect enter into commercial activity as a matter of choice, the limits they accept on their own conduct as a matter of conscience and faith are not to be superimposed on the statutory schemes which are binding on others in that activity. Granting an exemption from [statutory schemes] to an employer operates to impost the employer’s religious faith on the employees.To break out that last bit a little: In other words, a corporation is afforded the legal fiction of personhood, and therefore is separate from its owners--that's the whole jurisprudential basis for incorporation. The argument that the owner can assert his or her personal constitutional rights through the corporation, but not be liable for debts run up in the corporation's conducting of its business really would be allowing owners to have it both ways.
By incorporating his business, Potter voluntarily forfeited his rights to bring individual actions for alleged corporate injuries in exchange for the liability and financial protections otherwise afforded him by utilization of the corporate form. Adoption of Potter’s argument that he should not be liable individually for corporate debts and wrongs, but still should be allowed to challenge, as an individual, duties and restrictions placed upon the corporation would undermine completely the principles upon which our nation’s corporate laws and structures are based. We are not inclined to so ignore law, precedent, and reason.
Also, of course, the constitutional claim for any exemption is, as I have pointed out (more than once, I must admit), is quite weak, in the wake of Employment Division v. Smith (1990). There is, of course, RFRA, but the constitutionality of RFRA is far from clear (is it an impermissible establishment of religion, to extend greater privileges than constitutionally required? Unclear). As is the application of RFRA to the exemption at issue--is the cost involved sufficiently weighty and proximate to an act the employers believe to be inherently sinful as to amount to a substantial burden on expressing religion? And if so, does conscription violate RFRA? Taxes? Quite neatly, the fact that corporations are not their owners allows those questions to be decided another day.
(Hat-tip to LGM)