It's not biblical to "ostracize" someone who isnt tithing, but i believe when God gives a command, He provides a way for all of His people to obey. I see no exceptions to the 10% commitment, so i dont believe there are exceptions. However, I am not responsible for my fellow believer's tithe - I am only responsible for my own. Whether someone chooses to tithe or not is for them to deal with in their own heart. God makes it clear that NOT tithing is stealing from Him, so.... a non-tither should decide for themselves if they are okay with stealing from God, and if God is okay with them doing that. However, i dont see it in the Word as a reason to ostracize them.
1. God said all the tithes, (not some) were agricultural in nature; i.e., crops and livestock. Lev 27:30-34
2. God said tithes were only to be given to Levites, widows, orphans and foreigners in Israel. Num 18:21,24,26,28; Deut 12:1,10-11; 14:28-29
3. God said you were to eat your tithes with your family, your servants, and the Levites. Deut 14:22-27
If you will diligently study the tithe, you will find that God never amended His command for tithes to be money instead of agricultural products. Nor did He ever amend the command so that people not living in Israel would be required to tithe.
The problem is, too many today do not study the Word properly. Because of this, when their pastors teach for doctrine the commandments of men, they readily believe their pastors. See Matthew 15:9 for what God thinks of those who teach for doctrine the commandments of men.
God never commanded a monetary tithe from anyone.