Nausicaä of the Valley of the Wind

This is a 1984 animated science fiction film directed and written by the God of Animation Hayayo Miyazaki, based on his manga of the same name. It features a post-apocalyptic future where wars have devastated the planet. I couldn't really summarise it better than the Google blurb (as I haven't watched it myself):

Far in the future, after an apocalyptic conflict has devastated much of the world's ecosystem, the few surviving humans live in scattered semi-hospitable environments within what has become a "toxic jungle." Young Nausicaä lives in the arid Valley of the Wind and can communicate with the massive insects that populate the dangerous jungle. Under the guidance of the pensive veteran warrior, Lord Yupa, Nausicaä works to bring peace back to the ravaged planet.

The film is regarded as the start of the famous Studio Ghibli, being the first collaboration of Hayao Miyazaki and Isao Takahata.

The film features (according to various sources) themes of pacifism, environmental dangers, and looking after nature.

For those who find this important, the film has been dubbed in English, featuring voices of Alison Lohman, Patrick Stewart, Shia LaBeouf, and Uma Thurman (and if you aren't in already - Mark Hamill).

Now for the downside - it doesn't appear to be available on ahem suitable websitesit doesn't appear to be available for streaming on ahem suitable websites in suitable quality.

Tallying the bonus points:

• "Widespread societal angst of that time" - yes, for the theme of pacifism (1984, war, all that) - +1;
• "Societal angst of today" - yes, for the same reasons, and the environmental concerns - +1;
• "Realistic nature of the apocalypse" - yes, very much so (for the reasons above) - +1

Total: +3 bonus points.