How do you seal a wooden shiplap wall made of old fence boards?

It's for a cabin that's not heated in the winter. I want to keep it natural looking but I don't want it to get moldy. The boards were soaked in a bleach bath, dried in the sun and sanded before putting up.
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Just use a flat polyeureth.
Or use polycrylic. Polyurethane will yellow over time.
This is for sealing odors in wood. If it does that it should work well for your situation.
How to Eliminate Odors in Wood
Your best hope for sealing in any odors is shellac. It makes an excellent barrier coat over all wood species, and it sticks to almost anything. Zinsser makes a great product for this purpose, called Bullseye SealCoat. It’s a clear dewaxed shellac that you can apply to those drawer interiors easily with a brush. It dries quickly and should help to diminish mice, mildew, musty, smoke, urine smell. And since it doesn’t contain wax, you can apply other finishes like lacquer or varnish over it — they’ll stick just fine. SealCoat is also handy to have around the shop as a general purpose wood finish and sanding sealer. So, I’m sure you’ll find other uses for what’s left of the quart you buy.