If the perp was just there to steal something from the church, wouldn't the reason for the Swat gear would be to look like and pass himself off as LE if walked up on as Missy did? That's why I think he was there to kill Missy.
"If the perp was just there to steal something from the church, wouldn't the reason for the Swat gear would be to look like and pass himself off as LE if walked up on as Missy did?" ...Yes one logical explanation of why he was dressed as he was, would have been to steal things and then give himself a way to escape if someone discovered him.
Unfortunately, we don't know if perp did try to use the "I'm LE here checking on a break-in" ruse to get out, or not, before killing MB. He could have, and it simply failed. For example, what if, in a stroke of incredibly bad circumstance, MB happened to know him, and recognized him despite the outfit? That's one scenario, and there are many others we can create where MB wasn't fooled and perp then decided to kill her. But there were only two people there who know exactly what happened and why, neither are talking, so we just don't know.
The problem with the costume is that it doesn't tell us why perp went there -- it's a useful tool for ANY reason you might be trying to hide your identity. And once perp is illegally in the building, that criminal act by itself offers a motive to obscure identity, regardless of why else he might have been there.