The Constitution and "Islamic renewal"

Professor Friedman (Religion Clause blog) reports:

USIP Urges US Support of "Islamic Renewal"

Yesterday's Morocco Times covered a special report by Abdeslam Maghraoui issued recently by the United States Institute of Peace (USIP) in Washington. The report argues that the only way for the U.S. to effectively counter Islamic extremism is to back "Islamic Renewal", a growing social, political, and intellectual movement whose goal is a deep reform of Muslim societies and policies. The USIP is an independent, nonpartisan institution established and funded by Congress. Here is the USIP's summary of the report and a link to the full text of the document titled American Foreign Policy and Islamic Renewal.

I wonder . . . how does -- or how should -- the Constitution constrain the United States in its efforts to support "a growing social, political, and intellectual movement whose goal is deep reform of Muslim societies and policies"?  For example, is the purpose to promote, endorse, or instigate changes in Islam or in Muslims' beliefs and practices a "secular purpose"?  Are there limits on the ability of officials to promote what they regard as the true version of a particular religion, as opposed to a version that, it is claimed, has "highjacked" that religion? 

I have suggested elsewhere that -- for better or worse -- the content of religious doctrine and the trajectory of its developments are matters to which even secular, liberal, and democratic governments will almost certainly attend; and that it is not the case that governments like ours are, or can be, "neutral" with respect to religion's claims and content.  Religion shapes what people think -- it shapes their values, commitments, loyalties, priorities, etc. -- and so a government that depends (as many think ours does) on the formation of citizens with certain dispositions and capacities will care what religions teach.  Are they allowed, though, to try to change what religions teach?  If not, why not?