I think the impact of such phenomena has more to do with "governance" than with our understanding of the universe and whether other beings share it with us. The legitimacy of governments depends on their ability to "protect citizens" from enemies or intruders, and whether these "enemies" are humans or extraterrestrial does not make a big difference.
While the idea of God provided that "alien" element for centuries, regimes made sure to justify their actions and decisions on earth to be inline with the invisible god. God has always been hiding behind its messengers, but seems to have a place in human logic and thought as a plausible possibility. It is no coincidence that declaring the death of god coincided with another declaration, that is, we are alone in the universe and we should take responsibility of our existence and future - i.e the age of humanism.
The visibility of extraterrestrials, unlike god, makes their connection to earth experiential and more direct, without the medium of a messenger. The very same visibility seems to imply technological advancements, that they can appear to earthly beings at will. Human technology, on the other hand, operates in the realm of the six sense media, and sheds lights on our spatial awareness that earthly laws are not as fixed as we believe them to be. It is a matter of knowing how to manipulate such laws in ways that enhance our control over ourselves and surroundings. This paves the way to all kind of conspiracy theories and science fiction that there are elite groups, or secret societies, or governments who are more "in the how" than the average populace. As such, a congressional hearing becomes necessary to clear things up, or to strike a balance between transparency, alleviating doubts and keeping state secrets intact.
As to the relationship to Buddhism, polytheism seems more conducive to the belief in aliens than monotheism. Having different allegiances to different gods or extraterrestrial groups could explain why governments engage in endless conflicts over absurdities. Beyond the facade of national and religious narrative, they might be receiving some telepathic or even direct orders from their masters, where planet earth is a mere theater to solve rivalries between gods through their agents on earth!
Before leaving this to rest, a hybrid theory between gods and extraterrestrials can be easily overlooked. A god that is hijacked by aliens is not necessarily implausible. It is our habitual thinking that associate the term "god" with superior powers, but if s/he is a subject to impermanence, aliens can be even more superior by virtue of their ability to appear to earthly beings at will, whereas god is yet to demonstrate such abilities.
Allowing god to make contact with selected humans (prophets and messengers) seems to be a necessary condition for alien influence to be more effective moving forward.
And the Blessed One addressed the bhikkhus, saying: "Behold now, bhikkhus, I exhort you: All compounded things are subject to vanish. Strive with earnestness!"
This was the last word of the Tathagata.