Is there an expression that sums up "improperly conflating two ideas that are really separate issues"? [closed]

I'm intrigued by a local sign-holder who was improperly labeled "atheist" for carrying a sign that asserted that there was no after-life for a person's consciousness. The person expressed a belief in God, but not belief in the immortality of the soul. Is there a short, crisp way of saying: "You are incorrectly characterizing disparate ideas as monolithic"?

Solution 1:

Mixing apples and oranges

1.(idiomatic) To mix two totally different things. Related terms: (like) compar(ing) apples and oranges

Source: http://en.wiktionary.org/wiki/mix_apples_and_oranges

Solution 2:

Concluding that someone doesn't believe in God just because they don't believe in the immortality of the soul is a non sequitur.

Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises. In a non sequitur, the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion.

Solution 3:

There's always the somewhat pedestrian lump.

to deal with, handle, consider, etc., in the lump or mass: to lump unrelated matters indiscriminately. (Dictionary.com)

Depending on how it's used, it can carry the connotation of inappropriate aggregation. In the example case, I'd say your name-caller is lumping the sign-holder in with (or together with) atheists.