You are granting those institutions a privilege, they are exempt, for some reason, from the duties other organisations have. That certainly constitutes "support", doesn't it?
Nope, not 'granting' anything. Organizations don't have 'duties' in this context. The people, through its elected representatives, chose to levy taxes on individuals and corporations and, in no small part due to Article I, exempted religious organizations from taxation. That is not 'support' in my book, simply adherence to the Constitution.
How religious organizations use the money they collect & earn from investments should be considered in whether they qualify for tax-exempt status in my opinion. For instance, the money spent by the Mormon Church (and other organized churches) campaigning for California Prop 8 should disqualify them - separation of church and state (a whole 'nother subject, not related directly to taxation) is or should be a two-way proposition and if religious organizations want the power to influence political issues with their money, they should be prepared to be subject to the same laws as the rest of us.