A postal vehicle can be stopped by police ... but when they are stopped they must be let go within 15 minutes or be charged with delaying the mail service 18 U.S.C. § 1701–1703
This would be enforced by a postal inspector and moved to a federal prosecutor (US Attorney) and the charge bypasses all qualified immunity.
For this reason the police almost never mess with postal vehicles.
Source: I got stopped in a postal vehicle by a state trooper for bypassing a weigh station ... it went really badly for the guy.