Where you live the soil is very alkaline and adding ashes makes the soil even more so. Green oak leaves are very acidic but dead leaves and leaves that are breaking down are only slightly acidic to neutral. Coffee grounds are usually slightly acidic with a Ph of about 6.7 but depending on the coffee grounds can be neutral. In Boerne you need all of the acid you can get and hardwood ashes here have a Ph of about 10, so adding ashes is not a good thing at all.
Situational internet strikes again. I have acid clay and love ashes but I would not put them in compost while in the pile. I would mix them with soil. There in nothing left to eat in ashes so it would starve a pile actually since they are alive basically.
It depends a bit, ash from coal fires is not good, but wood ash is a good source of potash, good for flowering plants, and on the top of the compost heap it is unlikely to wash straight through. The OP was advised against it because it is alkaline, and he lives in an area with highly alkaline soil, that would not apply where I live, it is fairly acidic. Mine has gone on my garlic bed, garlic likes alkaline, but now they are starting to sprout it will go into the compost.