I was able to save a Log entity manually which was meant that the database connection was good. Before giving up, I came across issue #1 which explained the problem.
It would be very helpful if you included the WithFilter configuration in README.md and made a brief mention of the issue as I'm sure it would help others in the same predicament.
In addition, as this is a known issue, wouldn't it be a good idea to include the following code in the WriteMessage method in EntityFrameworkLogger class?
if (!this.Name.StartsWith("Microsoft.EntityFrameworkCore"))
context.SaveChanges();