Soap likely won't solve things; it'll only mask the smell for a while. But there's an old, reliable anti-mildew formula that works well on tents. I've given the same advice before, but there's no harm in reiterating it.
First, kill the mold with a solution made from one-half cup of Lysol mixed in with a gallon of hot water. Then, rinse the material with a solution comprising a gallon of hot water mixed with one cup of lemon juice and one cup of salt. Allow the tent to dry, then soak the stains in another batch of the lemon/salt/water solution. That should get the stains out. Rinse thoroughly and allow to dry. Do NOT put your tent in a clothes dryer, as the heat will cause the waterproof coating to peel off, and then you'll have real problems!
The best way to prevent this problem in the future is to keep the tent as clean and dry as possible. Damp-sponge it thoroughly after a trip, air dry, then store loosely in a mesh bag.
Support Outside Online
Our mission to inspire readers to get outside has never been more critical. In recent years, Outside Online has reported on groundbreaking research linking time in nature to improved mental and physical health, and we’ve kept you informed about the unprecedented threats to America’s public lands. Our rigorous coverage helps spark important debates about wellness and travel and adventure, and it provides readers an accessible gateway to new outdoor passions. Time outside is essential—and we can help you make the most of it. Making a financial contribution to Outside Online only takes a few minutes and will ensure we can continue supplying the trailblazing, informative journalism that readers like you depend on. We hope you’ll support us. Thank you.