People sometimes use "political-savvy" to describe someone who is aware of what to do or what not to do in an organization or company. I wonder which word would be the opposite of that? i.e. someone who doesn't have that set of political (business, communication) skills.
You could go with "political-naïveté", where naive is an antonym for savvy.
na·ive [nah-eev] adjective
1. having or showing unaffected simplicity of nature or absence of artificiality; unsophisticated; ingenuous.
2. having or showing a lack of experience, judgment, or information; credulous: She's so naive she believes everything she reads. He has a very naive attitude toward politics.
Source: NAIVE. (n.d.). Dictionary.com Unabridged. Retrieved April 18, 2014, from Dictionary.com website: http://dictionary.reference.com/browse/NAIVE
As a bonus, savvy and naive both have roots in the romance languages, being primarily from Spanish/French and French respectively.
I've heard the term "politically inept", as an adjective. There's even a Simpsons episode that uses this phrase in its title.
Unfortunately, the noun form, "political-ineptness" or "political-ineptitude", is not very elegant.
Do-nothing: always used before a noun 1 : not willing to work, help, etc. : lazyenter link description here
a do-nothing husband
2 : failing to achieve or do anything important
a do-nothing policy/government/politician