I prefer to have my fabric cut.
I've been tearing 15-18 inch lengths of muslin off the six yard piece I bought for the "Dear Jane" blocks i've been making - it really doesn't seem to afflict it very much and I've been able to press the ends so they aren't ruffled.I estimate that I'm losing less than 1/4 inch on each torn end.
In my opinion, the grain of the fabric is the grain of the fabric regardless of whether it's cut or torn. When it's torn, the crosswise grain is more obvious, but tearing it doesn't make it straight if it's off-grain to begin with.