What's a word that means does not belong, and doesn't matter at the same time?

Solution 1:

I think you might be looking for

irrelevant adj
Unrelated to the matter being considered.

TFD

Solution 2:

The term inconsequential should cover your intention:

1 a : illogical
   b : irrelevant
2 : of no significance : unimportant
_{(Source: Merriam-Webster)}

But, there is also extraneous:

2 a : not forming an essential or vital part <extraneous ornamentation>
   b : having no relevance <an extraneous digression>
_{(Source: Merriam-Webster)}

So, in your sentence:

... Or is that car photo inconsequential?
... Or is that car photo extraneous?

Solution 3:

I think non sequitur might fit your needs:

a statement having little or no relevance to what preceded it; a conclusion that does not follow from the premises. -TFD

Also, immaterial is a possibility:

of no importance or relevance; inconsequential or irrelevant; of no essential consequence; unimportant. -TFD

Is this a joke because you're from the south? And this seems weird to you. Or is that car photo a non sequitur / immaterial?