There's been a lot of hype and disinformation.
(Part of this is because Oracle owns Java now; indeed it's widely thought that Oracle bought Sun just for Java, really. And whereas lots of people liked Sun, which was a pretty good citizen of the FOSS community, everyone hates Oracle, which isn't.)
On Linux, you're still fairly safe.
You need Java for LibreOffice, as you note.
If you're still on IcedTea 6, I'd suggest that you update to IcedTea 7 - it's in the repositories. Keep your computer(s) scrupulously up-to-date, and if you're feeling really paranoid, just remove the icedtea-?-plugin package; this will leave Java installed on your computer (for local Java apps) but disable it in your web browser.