My two cents: A Church can certainly teach a particular perspective on such issues, but I would hesitate to teach them as undeniable doctrines of the Church that must be obeyed...or else!
I actually embrace the concept of tithing. Why? There are several reasons...but I don't have time to list them here (nor do I suppose that this is the rationale for this thread). Yet I would not point the finger of judgment at those who do tithe...or don't tithe. I do not think that a Church should base membership or judge the spiritual condition of a man based on whether he gives 10% of his income or not.
When it comes down to it, none of us tithe in the strict, Old Testament sense of the word. Tithing wasn't limited to monetary income. It encompassed farm products, gifts, crafts, etc... Last I checked, I didn't know of a single person who brought a tenth of their apples...oranges...or puppies to the "house of God." Of course, the "tithe" wasn't used in Biblical days for what it is used today (to pay for the buildings, equipment, utilities and salaries of our modern Church institutions).
I guess it would be better to reword the discussion. Should a Church establish a requirement like tithing? Should a Church establish such "required" doctrinal principles toward those who wish to be a part of a local congregation?
If something isn't entirely clear from Scriptures...for New Testament believers...and there are rational reasons by which a believer holds to a belief...should such a believer be barred from entering open fellowship with a local congregation? I have been to congregations that would kick out people for the most ridiculous of things!
:-o