Should I ignore Google’s rendering issues?
I'd take them seriously as much as I can.
... However, the site is getting indexed as unique content to our site is easily searchable.
I have noticed that the cached versions of our pages is just the pre-js splash screen.
Also, on http://www.webpagesthatsuck.com/does-my-web-site-suck/does-my-web-site-suck-checklist-part-one.html the author mentions in the checklists for bad website design:
I'd suggest going over the entire checklist, making sure your site doesn't score any check marks in that list then test it again with the google bots.