Oh no its not, the subject of aliens has been long declared as heresy in the Catholic Church. Ever hear of a guy called Giordano Bruno, a heretic who was burned at the stake for refusing to repent on heresy?

In 1588 Bruno, wrote the following in his 5^th dialogue of On the Cause, Principle, and Unity: 'I can imagine an infinite number of worlds like the Earth, with Garden of Eden on each one. In all these gardens of Eden, half the Adams and Eves will not eat the fruit of knowledge, but half will. But half of infinity is infinity, so an infinite number of worlds will fall from grace and there will be an infinite number of crucifixions.’ --- As quoted by Martinez in Burned Alive.

Here we can see the endless heresies inherent in Bruno’s works, endless Adams and Eves, sins and many Christs. In Martinez's book burned alive he details every aspect of Bruno’s beliefs, the 54 heresies and philosophies he was accused of during his long trial by the Inquisition. In most cases, Martinez tells us, Bruno was able to argue his way out of them, one way or another, but refused to retract 13 of them on the subject of substance, that the Earth has a soul, that there are many occupied worlds etc. For these heresies then, Giordano Bruno was burned alive, ‘inflicted for the gravest offenses. Other theologians too cited this heresy for centuries. They explained the problem: “we cannot assert that there exist two or many worlds, since neither do we assert two or many Christs [the only begotten son]”

In 748AD Pope Zachary I declared heretical the belief that stars were suns with similar worlds like Earth and that on these are other intelligent beings like mankind. Rejections of these antipodean heresies are also to be found in early medieval writings. In 1459 Pope Pius II again condemned the doctrine ‘that God created another world than this one.’    
 

Martinez tells us ‘St Hippolytus [170-235AD, a martyred Christian theologian] ridiculed the doctrine of infinitely many suns, moons and worlds, some inhabited.’ The Professor tells us: ‘around 260CE Pope Dionysus of Alexandria wrote a tract against the Epicureans mainly to criticize their theory that all things were composed of atoms without divine Providence.’ Martinez explains this was directed against the theory that atoms clash and combine by chance ‘and thus gradually form this world and all objects in it; and more, that they construct infinite worlds,’ The book also shows us there were many Fathers of the Church who condemned the claim that there are many worlds like ours. He records that ‘in 384CE’ Philaster, Bishop of Brescia condemned the ‘heresy that says worlds are infinite and innumerable…whereas Scripture says that the world is one and that it teaches us that it is one.’ In 402 St Jerome complained that one of the most heretical claims of all was that ‘worlds are innumerable.’ St. Augustine even composed a list of 88 such heresies; the 77th was that ‘worlds are innumerable.’

Modernism personified. Sure you could apply the same quip to those who believed in Christ and the Church He founded.

Your response to the Church's history on aliens was:
'Once upon a time many people thought that the world was flat and that if you went too far you would fall off.'

I took that to mean the Church's teaching on aliens as heretical was somehow related to the flat-Earth belief and thus nonsense. Thus I named it 'Modernism personified.'

I am now trying to figure out the above response. It could mean that the Church teaching is still the same even if 'science' has advanced. I would agree that the Church's teaching cannot change, does not change, and remains the same. As for 'science may advance' well what advances has it made on the subject of aliens? Are you suggesting science has somehow advanced that aliens exist? If so we would all love to hear about it.

 https://philos-sophia.org/scientism-ideology/

Here is what Wolfgang says if it doesn't open:

A great deal of what we call science is scientism,  which is to say that it’s ideology driven.  What we are facing here is not “science,” properly so called, but a kind of “religion” you can say. It’s something people are passionate about. It’s something they defend, and it is something for which they are willing to attack.  So a great deal of our so-called science is ideology. And, in fact, it is the ideology which is presently manifesting in all the different cultural domains of our civilization, including the political. [and Pouch's Modernism]