You are 'officially' welcome to park at the resort you are paying to stay at....for as long as you want. You aren't 'officially' entitled to park, while in a park, at a resort you are not paying to stay at. So...what does this mean? It means that Disney prefers that you park at a resort if you are enjoying the amenities of that resort...eating, shopping, checking it out. But, that doesn't mean heading to a park for the day. Just because you are staying elsewhere, on-site, doesn't mean you get to park at every other resort for the day, while you head to a park. That is a perk that those paying to stay at these resorts are getting...as well they should for the money they are paying to stay there!!
Can you park at the Polynesian, for the day, and go to a park after eating? Sure. It will most likely be allowed. It's really more of an honor system. If you do choose to park in a resort that isn't the resort you are staying at, for the day, it would be polite and considerate to choose a parking spot that is a bit further removed from the front of the lot.
There will be times during the year that you won't be allowed to park.....for instance, during Food and Wine times, parking is limited at the Epcot resorts. If you aren't staying at, for instance BW, you won't be allowed to go to the general parking area. On the nights of
MNSSHP and
MVMCP, you may find parking to be limited at the CR and the Polynesian. There will be signage up at the resorts letting you know that parking at the resort for theme park access is not allowed.