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I had never seen anyone stop for a funeral procession until I visited relatives in western NC. It just doesn't happen around here unless the police block a traffic light or stop sign so everyone can stay together.
In the OP's case I would have continued on also.
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In most southern states the law requires you to stop for a funeral procession, and the cops providing escort will give tickets to those who don't. I honestly don't think it applies on divided highways and interstates, but on lessor roads, it is the law.
ETA: Don't worry about stopping for mine, my family has strict instructions, I am to be cremated, no services, and my ashes are to be thrown into the nearest dumpster. Once I am gone, I am gone, and while I certainly won't care, don't want anybody getting hung up over it.