Like TAS it isn't considered canon in Star Trek...
That hasn't been true since Gene Roddenberry died 22 years ago. TAS has been repeatedly referenced in canon since then (particularly "Yesteryear," which was referenced in TNG: "Unification" and inspired the young-Spock scenes in the 2009 film), the novels and comics have been free to use its characters and ideas, and the "canon-only" websites Startrek.com and Memory Alpha include it right alongside the other shows.
I can ignore the animated Godzilla series.
Well, considering that the Toho Godzilla franchise already has, like, seven different continuities, there's no need to ignore or de-canonize anything -- just treat them as parallel realities. In my blog article reviewing the franchise
a while back, when I made a list of all the continuities, I included one that comprised the '54 film, the '98 film, and GMK, and another that included the '54 film, the '98 film, and G:TS.