> Wouldn't we then expect homicide rates in religious USA and Pakistan to be much lower than in secular Sweden?

If you were able to control for all other conditions, possibly but not necessarily. Thus I don't think comparing homicide rates in the USA, Pakistan and Sweden proves or disproves anything.

First, you grant that other conditions have influence too, and not only as much, but more influence, than religious beliefs.

So, comparing homicide rates across countries disproves that more religion is necessary or sufficient for an ethical life.

(Let me note in passing that fairly secular northern Europe also has much lower rates of abortions, STDs, teenage pregnancies, and other societal ills, than other, more religious societies.)

Second, if we look at long term trends, violence has come down over the millennia, as religiosity has decreased (see Pinker's Better Angels).

Third, I concede that under certain circumstances in primitive societies you might achieve a reduction in crime by introducing certain religious beliefs (whether they're falsehoods or not). However, we should not strive for that, but for enlightened societies where that is not necessary anymore.