Incest is probably bad.
Unsurprisingly, Tumblr doesn't seem to think so.
Incest in Doctor WhoEdit
Coming from such a small, insular community that had degenerated due to an ill-conceived (ah? See what I did there?) eugenics program, Leela was a product of incest.
Amy Pond regularly committed sexual assault against the Doctor, who would eventually turn out to be her son-in-law (twice over!). Likewise, River's implied to be the Doctor's daughter numerous times, and is kiiinda the TARDIS's daughter, and the TARDIS is the Doctor's Wife, and none of that stopped them from getting hitched. Conversely, Rory Pond is the only man River Song never hit on, though everything she ever said indicated he's totally her type.
Incest is somewhat common among human royalty, but Doctor Who seems to particularly focus on the ones who married their siblings (Nero, Cleopatra, Nefertiti, alternate-timeline Erimem) or at least first cousins (Victoria, John). The closest you get to non-incestuous royals is… Kublai Khan, who only married a cousin-in-law?
The Osirans committed incest as their routine reproductive custom (well, sort of; they were the most powerful psychics in the Universe, so they made babies with their minds, meaning that they probably kind of had to use siblings in order to reproduce; that's not going to stop Tumblr from making Osiran dick porn the minute they figure this out though).