So simply put, you're claiming a regulation can trump the constitution. Brilliant. :)
No, those are the words you're putting in my mouth. I'm saying those regulations were written with past Supreme Court decisions in mind. The most relevant decisions are:
Rutan v. Republican Party of Illinois (88-1872), 497 U.S. 62 (1990)
"A government's interest in securing employees who will loyally implement its policies can be adequately served by choosing or dismissing certain high-level employees on the basis of their political views."
(The court found that most politically based firing was impermissible, but 'certain high-level employees' were excepted.)
BRANTI v. FINKEL ET AL. 445 U.S. 507 (1980)
"On the other hand, it is equally clear that the Governor of a State may appropriately believe that the official duties of various assistants who help him write speeches, explain his views to the press, or communicate with the legislature cannot be performed effectively unless those persons share his political beliefs and party commitments. In sum, the ultimate inquiry is not whether the label "policymaker" or "confidential" fits a particular position; rather, the question is whether the hiring authority can demonstrate that party affiliation is an appropriate requirement for the effective performance of the public office involved. "
This repeats the majority opinion in ELROD v. BURNS, 427 U.S. 347 (1976)
"A second interest advanced in support of patronage is the need for political loyalty of employees, not to the end that effectiveness and efficiency be insured, but to the end that representative government not be undercut by tactics obstructing the implementation of policies of the new administration, policies presumably sanctioned by the electorate. The justification is not without force, but is nevertheless inadequate to validate patronage wholesale. Limiting patronage dismissals to policymaking positions is sufficient to achieve this governmental end. Nonpolicymaking individuals usually have only limited responsibility and are therefore not in a position to thwart the goals of the in-party. "
In other words, political appointees may be removed at will. Most government employees cannot. Now stop playing at being a lawyer; it looks really bad when a mere amateur shows you up.