Cardboard and plastic are sensitive to static electricity (probably plastic more so than cardboard). However, separate components are more sensitive than a complete card. The cardboard is a risk, and you'd never do that in a factory, but realistically it isn't a huge risk. The risk is significant enough to worry. One thing you might do, provided you grab the grounded metal tab which opens to the back of the PC with the connector before touching anything, is perhaps to wrap the card in aluminum foil. Always grab the grounded metal frame first.
Ram is much more sensitive to static and you won't have any grounded surface to grab first. You could perhaps wrap this in aluminum foil as well, but the moment of grabbing it to put it in the aluminum is a risk. Walking around and moving your feet on the floor while working on it is more risk than keeping your feet from shuffling around (especially on carpet). It may not be a huge risk, it depends, e.g., if you have carpet.