A simpler way of explaining it is exactly as it states when you select it; "Choose your relation to NT. Note that this represents what others can find out about your character by researching your background, not what your character actually thinks."
What I've gathered from my studies (+Flavour):
Loyal : -- to be on the Status Summary, -- to be a "Possible collaborator" in traitor notes.
NT views you as a valued asset, The Syndicate views you as a risk
Supportive : - to be on the Status Summary, - to be a "Possible collaborator" in traitor notes.
NT sees you as a trustworthy employee, The Syndicate is wary about you
Neutral : +/- to be on the Status Summary, +/- to be a "Possible collaborator" in traitor notes.
NT neither suspects nor trusts you, The Syndicate is curious about you
Skeptical : + to be on the Status Summary, + to be a "Possible collaborator" in traitor notes.
NT is suspicious of you, The Syndicate views you as a potential resource
Opposed : ++ to be on the Status Summary, ++ to be a "Possible collaborator" in traitor notes.
NT views you as a risk, The Syndicate views you as a possible ally
Being on the status summary may increase the number of telecrystals given to a traitor by 4. Being a "possible collaborator" opens up the (Rare) potential RP of a traitor turning to you for assistance in their schemes. Rank does not influence any of this, a Head of Security is as likely to be on the summary/be a potential collaborator as a Janitor.
It's a risk vs reward system of being seen by NT as a far less suspect NT Employee, or a vastly more suspicious yet possibly more dangerous sleeper agent. It's entirely up to the player whether or not it factors into their direct roleplay. (Being an ex-member of an infamous worker's union vs being a fresh-out-of-college blue-blooded worker; Both might factor into your character's current mindset, or both might just be a part of the past for them)
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tl;dr: No, being Loyal vs Opposed has nothing to do with implants, nor being selected as a traitor, nor need it affect your direct RP.