I go to a Catholic mass every week. Why? The spouse goes and I go to keep marital harmony.
Just like the unbelieving mates of all those JWs people here make fun of--the ones who go to the KH but won't join. (including me on occasion, sad to say-- )
The first time I went I really was nervous, like I thought they could tell I was not one of them. No one paid me the least attention and everyone was very nice. The weirdest part is the Eucharist. That is done every week and done at the end of the service. I was amazed they did weekly (daily if you go) what the JWs only do yearly at the Memorial. I sit and stand when everyone else does and that's it. I don't say anything, including *amen*.
It lasts one hour and I am giving up so little of my time. I sit and think about other things-I meditate and realize I don't believe any of it and how glad I am I am out. At the same time I am very respectful because I wouldn't want anyone to think I am there to mock or just get info for making fun or anything like that. I am simply spending time with my family.
Since I haven't turned into a pillar of salt or anything like that, I can only conclude that Jehovah has better things to do than worry about people going into other places of worship.