[TestMethod]
public void CompareStringToDate()
{
    //Arrange
    var classA = new ClassA { ThisIsMyDateTime = DateTime.Now };
    var classB = new ClassB { ThisIsMyDateTime = classA.ThisIsMyDateTime.ToString() };

    //Asserts
    classB.Should().BeEquivalentTo(classA,
        options => options.ExcludingMissingMembers()
            .WithAutoConversion()
            .Using<DateTime>(ctx => ctx.Subject.Should().BeCloseTo(ctx.Expectation, 1000))
            .WhenTypeIs<DateTime>());
}

private class ClassA
{
    public DateTime ThisIsMyDateTime { get; set; }
}

private class ClassB
{
    public string ThisIsMyDateTime { get; set; }
}