If you Google 'Vatican and Aliens', you will find a number of references to Vatican officials making positive remarks about extraterrestrials - including a few who outrightly assert that they exist. In addition, the Vatican is interested in observatory time used for locating earth-like planets.
In summary, it looks like they wish to be prepared, come what may. This contrasts with Witlesses who would likely become hysterical and scream "Demons!".
OTOH, it is worth considering that, perhaps, the WTS is becoming prepared for profoundly negative events by selling everything off and hiding in their upstate NY country club.