After using the gun, be sure to remove all cartridges and allow the sleeve, sling or pouch to dry for several days.  As soon as leather products get wet from rain or high humidity, remove them from the gun and dry them, but not under the influence of sunlight.
It is also recommended to remove cartridges when storing the gun for a long time. Store the gun with the leather accessories in a dry room with less than 50-60% humidity. Read the rules for storing the gun in the instructions for it.
To reduce the absorption of moisture into the leather, use universal waterproofing (water repellent) sprays (the same as for shoes). Process leather, suede,  lacing and ammo loops (inner side of them too). Do this before each use. Such sprays protect products from dirt as well.
Use wet wipes to clean leather and suede. In case of heavy contamination, you can wash off the dirt with a stream of cold water. After that, dry the product and treat it with a water-repellent spray. You can use colorless protective creams (like shoe creams) but this can affect the color of the leather and suede.