Thanks for your suggestions. As I've continued to mess with this, and based on your suggestion to look at other internet accounts, it seems that my understanding of the relationship between my iCloud/Apple accounts (email, contacts, calendar) and the Exchange accounts is more complicated than I realized and may be part of the birthday entry problem. (I will note that one of the first things I thought to check was the Date/Time setting on my mac; it's fine.)
So, here's what I've discovered and the questions I now have:
1: The problem is only on my mac, not my iPhone.
2: In looking at my contacts on my mac, iPhone, and iCloud, I discovered that my lists of contacts on my mac and iphone matched but did not match those on iCloud (far fewer contacts there).
3: As to your suggestion to consider other internet accounts, I do have an email account that runs through a Microsoft Exchange server. On both my mac and iPhone, the Exchange server was set to access Mail, Contacts, and Calendar (which I didn't think I had set that way, but apparently did at some point in time). When I turned off access on my mac to contacts and calendar, leaving only Mail for the Exchange server, I lost all of my contacts except those that appeared in iCloud. Turning contact access back on for the Exchange account restored all the rest of my contacts, though they are now listed separately under the Exchange server (which had previously not been the case.)
4: Further checking shows that on my iPhone I have the Exchange account set as my default account for Contacts. I'm thinking that ages ago, when I first purchased an iPhone, my primary email account at the time was the Exchange account. Since then I began treating my @icloud email as my primary email account but never thought to select it as my default account for Contacts each time I upgraded to a new iPhone.
5: Meanwhile, the birthday settings, which I (once again) reset earlier today, seem to be holding. Can't tell you exactly what I might have done to fix it, if it is, indeed, fixed. Fingers crossed...
So...questions that I now have:
1: How might the Exchange account cause my original problem of having an extra day added to birthday entries in Contacts and their subsequent incorrect entry into Apple's birthday calendar?
2: Why would settings that are essentially the same for the Exchange account produce one result on my iPhone (birthday dates entered and recorded properly) but not on my mac?
3: What disaster might befall me if I change my Default account setting for Contacts from Exchange to iCloud? Or would it simply mean that going forward all new contact entries would show up in my iCloud Contact list?
Again, thanks!
