It's not "rude," but it may be dangerous for the residents of that neighborhood. "Rude" would be using a private community's private road to avoid traffic. "Rude" would be cutting through a gas station on a corner intersection to avoid waiting at a red light. If a road is a public road, built to a certain specification (design speed, width, height clearances), then it is wasteful to
not use it to it's slated capacity. There might be miscommunication between the Engineering Bureau and Urban Planning Bureau as to the road's/neighborhood's purpose , but that's a policy issue, not an obligation for private citizens to uphold.
The answer here isn't to tell private citizens "don't go here", or for private developers to add carve-outs into their apps for these roads, but to put pressure on politicians and budgetmakers so that they build better transportation infrastructure for all people.
(Personally, I think that private communities in the USA are a ridiculous idea, and are vestiges of codified segregation and redlining practice. Just using it here as an example.)