My parents are getting up in years. How important is it to find out what their wishes are? Is that invading their privacy?

That is a reasonable invasion of their privacy request on your part and should not be considered an invasion of their privacy. Presumably, your parents will pass away before you do. You need to know what their wishes are for the disposition of their assets. Discussing this with an attorney can avoid bickering among survivors, preserve peace in the family, and insure that the beneficiaries are those desired by your parents and that the amount that each beneficiary receives is consistent with your parents' wishes.