I agree with the new policy. = I am for the new policy.
Usually if we say "agree upon" a policy, two or more people will discuss it, then decide on the best policy. It is an event, not a statement of being for the new policy.
"The group met and after some discussion, agreed upon the new policy."
"I disagree with the new policy" is correct
You would never say "I disagree upon the policy."
He is going to visit the USA in July. [This is a period of time, without a particular day - it means sometime within the month of July]
He is going to visit the USA on July 2, 2012. [This is a definite day, so it is "on"]