Gypsum does not change pH as much as dolomite lime. It is however useful for making hard clay soils more workable but it is usually not needed unless you have saline sodic conditions.
Chicken manure has a lot of calcium. Enough to to raise the pH of the soil by a half a point so be careful adding it to alkaline soils
Comfrey,borage and some cabbages mineralize calcium from the soil and comfrey adds calcium when it is added to compost.
If you are using organic materials like plant residues, composts, manures, bone meal, bat guano, and green sand you need to be careful how much you add. Although these are natural or mined products they may contain salts, and unlike synthetics their analysis will vary a little from batch to batch. It is hard to get a pure element from organic products and the release of the elements is usually slow, but not in a controlled way.
Organic composts can buffer the soil pH up to a point and it can sequester some of the nutrients for a while.
You can go overboard even with organics so it is still good to do a soil test once in a while to make sure you stay on track.
Happy gardening in Hawaii. Gardens are where people grow.