Long story, short: It would have to be sentient life in order to get any long-lasting attention. In the recent past, plenty of scientists were sure that simple life (e.g., lichens) existed even on Mars. The general public didn't go nuts over that. So finding simple life—for sure, this time—wouldn't change anything this time around, either.
If the Great Filter is ahead of us, becoming a space-faring civilization sooner increases the odds of surviving it.
(And that's the main argument for the Great Filter being behind us, it is hard to imagine that we are fighting against astronomical odds to become space-faring.)
The argument the great filter is ahead of us though is based on the observation that even with slower then light spacetravel, over the timeframes of the existing universe a species could still colonize the entire Milky Way in something like a 100,000 years with von Neumann probes (of which organic life would be a good basis for building one).
There should be life everywhere it's possible by technological panspermia - but we don't seem to observe that. What stops elder civilizations from doing this, is the big mystery.
Unless of course, as a poster above notes, if we fire up the JWST and discover chlorophyll-fringes in the spectra of just about every rocky planet we can see. That'd imply a lot.
I posted this above, but it's a good answer to you as well.
I think that most people, be them scientists, religious leaders, politicians, or even laymen, will have their lives changed forever by the discovery of extra-terrestrial life. For the religious, discovery of even extra-terrestrial bacteria will upend most of the interpretations of their holy books. Those books are the foundation of modern Western society (Do not kill, do not steal, do not take another man's wife, etc). By upending the basis of society we have no idea how humanity will end up. Will we throw everything based on the bible away? Reinterpret them? Will the Jews and Muslims reconcile? Will the Christians set out on another crusade? Will that crusade be to the extra-terrestrial bacteria to wipe them out as well?
Doesn't surprise me at all. There are a multitude of opinions. But the question was "what will change", discussing those that accept the new findings and have no need to change is orthogonal to answering the question.
Some will outright deny the existence of the new information about extra-terrestrial life.
But, for most believers, I bet there will be a re-articulation of the tenets of the faith, a transformation of their existing doctrine into something that seems compatible with the new information.
Maybe this is not quite the right way to look at it, but it seems to me that, taken together, these religious faiths have already survived many, many highly traumatic historical and informational challenges and persecutions (e.g. invasion of the "sea peoples" in the Eastern Mediterranean, rise and fall of the Greek Empire, rise of the Roman Empire, destruction of the temple in Jerusalem, Constantine's conversion, religious councils which redefined Jesus, fall of the Roman Empire, Galileo, Copernicus, Reformation, Magellan, Enlightenment, British Empire, Darwin/Evolution, Napoleon, Hubble–Lemaître and modern cosmology, the Holocaust, etc ...)
For example, it seems to me like modern astronomy has drastically challenged and damaged the very notion of a saintly or holy figure "ascending into heaven," but believers whose holy books explicitly describe such an event have not abandoned their faiths in large numbers because of it.
Another example is modern biology and theories about the origin of humanity. That didn't stop religions based on the book of Genesis.
IMHO, hard evidence of extra terrestrial life will be just one more speed bump in the history of these faiths.