How about this:

SELECT Customer, [Type], DueDate1, DueDate2 FROM dbo.myTable mt

WHERE mt.[Type] = @Type

AND ((@Condition1=1 AND mt.DueDate1 BETWEEN @DueDate1 AND @DueDate2) OR (@Condition1<>1))

AND ((@Condition2=1 AND mt.DueDate2 BETWEEN @DueDate1 AND @DueDate2) OR (@Condition2<>1))

...or am I missing something?