A phrase of providing a non-committal answer

When you give a non-committal answer to a question that asks for a straight answer, you're "beating around the bush" or "being evasive"

beat around the bush - "to avoid answering a question; to stall; to waste time." TFD

"Stop beating around the bush and give me a straight answer."

evasive - "intentionally vague or ambiguous; equivocal, avoiding the issue; not straightforward" TFD

"As Williams' career progressed, his work became less and less evasive with regard to homosexual themes."

"You have to face the problem head-on and stepping right through it rather than being evasive and hiding from it in the hopes that it'll go away."

Given that you've mentioned politics or business, how about sidestep?

From Dictionary.com:

sidestep: to evade or avoid (a decision, problem, or the like)

Your example:

Person A: "I need to do A or B, which should I do?"

Person B: "A is very important and should be done, but B is also very valuable and should be taken into consideration"

Person B is sidestepping Person A's question -- that is, evading or avoiding answering it -- perhaps "to avoid responsibility or ownership of their response". Politicians, especially, do this sort of thing all the time.