Do relish recipes typically include vinegar?
Fruit relishes (including salsas, chutneys, and plain sauces like applesauce) can be made without vinegar.  But they almost always include some extra acid - if not vinegar, then usually citrus juice.

The acidity balances the sweetness of the fruit, and it preserves the color.

So you can make a fruit relish, substitute lemon or lime juice for the vinegar, and use it.  But of course, without a full pickling process, the fruit relish will only have a limited life in the refrigerator.