This is another bug. As you say, the 1776 date is for his father’s birth; it’s not date of this source. I’ll look into this as well and let you know once it’s fixed.
The issue is that the “1776” date is still stored as the date of the evidence. When you changed the source type from “Birth” to “Non-specific Source”, the system should have erased the 1776 date, but it didn’t. And since it’s a non-specific source, the date is not displayed or editable. The work-around is for you to edit the evidence, click on the Type tab and change the type from Non-specific source to Birth, then click on the Details tab and erase the date, then click on the Type tab again and change the type back to Non-specific source, then click on the Profiles tab and save the evidence. That should solve the problem. Would you please let me know if it does not?
I’ll change the system so that in the future if you change the evidence type to “Non-specific source”, the system will erase the date and place fields, which it should have been doing all along.