Let's discuss the intentional fallacy

Jack: Your breath stinks.
Jill: That's rude!
Jack: No it's not; your breath really does stink.

Jack is being:

(a) disingenuous;
(b) sincere;
(c) it doesn't matter; the fact is that telling someone their breath stinks *is* rude.

Tom: Women are stupid.
Tina: That's a sexist statement!
Tom: No it's not; all the women I know really are stupid.

Tom is being:

(a) disingenuous;
(b) sincere;
(c) it doesn't matter; the assertion that women are stupid, given the history of aspersions against women's intellectual equality with men, is a sexist assertion.

Brenda: Obama is a Muslim terrorist!
Brad: Given the fact that that statement relies on an implicit association between non-European names and violence, that statement is racist.
Brenda: No it's not; I wasn't even thinking that.

Brenda is being:

(a) disingenuous;
(b) sincere;
(c) it doesn't matter; given that the statement invokes on such an association, whether or not Brenda "meant" to do so, the statement is racist.

In all cases, (c) is the correct answer. Notice how nicely (c) frees us from having to divine the intent of someone who may or may not be fully honest about admitting to what is an acknowledged social gaffe. The point, in all cases, is that the statement in question is objectionable, regardless of the speaker's intent, because it the social context in which the statement exists makes it so. Whether or not one is aware of that social context and is being offensive "on purpose" is irrelevant.

See also. This too. Oh, and especially this.

You can issue as many denials as you want to, but the fact remains: in this society, at this historical moment, with this history, "that's not racist" is bullshit. It may be bullshit born of ignorance, rather than bullshit born of ill intent, but it is bullshit nonetheless.