Are all the usual disease outbreaks stoppable by wearing masks and washing hands, or is there one that will get you regardless?

Gloves, masks&Gowns: Gloves, masks and Gowns and Hand washing are usual isolation techniques but few infectios disease like Ebola you need to cover body and face as well and requires special clothes and equipment to be safe

Most of them: Masks are only moderately effective despite their being heavily promoted. While hand washing reduces transmission of bugs in the hospital, it does not stop them. Both are worthless for sexually transmitted, food borne and waterborne diseases.

Yes about 85%: Others have insect vectors like fleas / ticks / mosquito, Don't forget to boil water