how strict to be

No, 'strict to be' is correct, it's just a little awkward in this context. 'To be' in this context implys 'to become'. How about this?

They relish the freedom to practice Shiite Islam, but disagree over how strictly to follow it's tenets.

There is a sense of looking at the future here, that's where you got the 'strict will be.' It could also be written:

They relish the freedom to practice Shiite Islam, but disagree over how strictly they will adhere to it's tenets.

Both new versions are longer and maybe that it why the writer chose:

They relish the freedom to practice Shiite Islam, but disagree over how strict to be.

Joe

Nice. Joe Nation, thanks.

My pleasure. I always enjoy your posts. They make me think.