"Either ignore their anti-war, anti-American drivel and keep with the hobby, realizing they may have talent in one area and be clueless in another,"
I wouldn't have a problem with this EXCEPT, I cannot imagine that their cartoons are not drenched with the effects of their political affiliation.
In this case, it may not seem like leftist causes being promoted in the cartoons so much as a love of death---elevated to a level of "art". That love of death is part of the Left.
The only problem with your thesis is that much of the Anime, deals with Japanese issues. Also much that is being shown in the US is over 10 years old.
Cartoon network showed the "Gundam Wing" series (originally from the 80's) which contained several references to the Cold War.
There is a sense of fatalism in some Japanese anime. Some say that comes from the Hiroshima bombing.
I'm not familiar enough with pre/post war entertainment/literature in Japan to draw that conclusion.