Here is an example of the fallacy of compilation.
A good illustration of this fallacy is provided by a Mark Russell bit from the mid-80s when a bunch of LaRouchies managed to get themselves on the Democratic state ticket in Illinois (IIRC): "They say, 'We are for a strong defense'. OK, nothing wrong with that. But then... they segue into the Twilight Zone... 'We are for a strong defense, the construction of a national tinfoil shield, and the mandatory testing of goldfish for herpes.'"
By your reasoning, anyone who rejects the notion of stretching tinfoil over the continental United States is an opponent of strong national defense.