Dick and prick are every bit as much slurs as the others.
I realize that not everyone differentiates between words that are "pejorative" and words that are "slurs", but for me the basic difference is that in the case of the latter, the words in question are connected to larger patterns of (and reflect) marginalization of a particular group of people. I understand the inherent logical consistency behind the idea that calling someone a dick is similar to calling someone a cunt, as both are ostensibly implying that penises or vaginas are bad. But because (social context) dick is not connected with any larger pattern of marginalization (or otherization or discrimination), I do not think of it as a slur.
I think perhaps a somewhat analogous situation would be with differentiating between racism and prejudice. Racism is systemic and institutionalized, and these patterns create a racial hierarchy through their effects. Prejudice is reflective of an individual's thoughts and beliefs. So in this conception, if a minority behaves in a discriminatory manner against a white person, it may be reflective of prejudice (or bigotry, if you like), but it does not reflect racism.
The primary problem with the above analogy, I think, is
that, "One reason why, in general terms, whites and people of color cannot agree on racial matters is because they conceive of terms such as "racism" very differently.
Whereas for most whites racism is prejudice, for most people of color racism is systemic or institutionalized," and this means that there are probably quite a few people who will reject
both conceptions. But I hope that I have at least adequately explained how I am approaching this.