I found somewhat of a workaround, but it requires you use or create a Microsoft account - everything is free, though.
I installed Microsoft To Do on my Mac using my Microsoft account, and then on my iPhone I added that same account as an Outlook account under Settings | Passwords & Accounts and enabled Reminders. Now when I add reminders on Microsoft To Do from the Mac they show up in Reminders and MS To Do on my iPhone, and vice versa. You probably don't need to install To Do on your iPhone, but I just wanted to compare it with Reminders.
I realize this doesn't fix the issue with Reminders on the Mac, but I'm not able to upgrade to Catalina at this point and needed a workable solution so I went with this approach.