There's so many factors involved, that the answer for this becomes kind of tricky. To say if you'll get yeast infection from missing a single shower is not likely, but if you're going backpacking for several days or weeks without being able to shower and having very moist skin your likelihood increases several times. In other words, missing a single shower may not really be a huge problem, but regularly not bathing can definitely contribute to a change in your vaginal environment, and that will definitely lead to some form of vaginitis – including the possibility of a yeast infection. Remember, yeast loves dark, warm, moist environments. The longer you go without cleansing, the more you’re exposing yourself to free radicals and toxins in the air – all things that can alter your vaginal pH.
You can also get fungal skin infections from not showering, especially (but no only) if you’re overweight. Yeast loves the warm, moist environments caused by sweat, so you’re particularly susceptible to rashes under your breasts, in the folds of your skin, and – for men – in the genital area.
Remember to at least bring several fresh pairs of underwear, and change them into dry ones as soon as possible. Often times women will try to use baby powder to keep the area fresh and dry, but be very careful. Women shouldn't use talc powder down there, although they can use it for other areas like armpits, and yeast will also flourish on corn starch. When in doubt, seek medical attention for the right diagnosis and treatment plan for your individual condition.