The biggy here if we come to know with absolute certainty that life exist even in the most microscopic of forms somewhere out there, it is an incredible paradigm shift in current thinking of our place and space in this cosmos. Many religions will have to rewrite or manipulate their current creation stories to fit the new science.
With regard to "alien" visitors to this planet, I am of the belief (it's just my gut feeling I can't prove it, I just have experienced it) that the material world as we know it is just that. As we go about breathing air in these bodies of ours we are trapped within a dimension we call space and time. I believe whole heartedly there are other dimensions right here in the now that we can't see or be aware of. We can't experience them because we are in a dimensional prison. Take some shrooms / deep meditation and you are able to get a peek but still not be able to get out there. I have no proof but suspect the energy within us...our life force is able to cross into dimensions we in our material form can not. As such traveling billions, trillions of matter miles can be done in a millisecond. Just conjecture, not science based hope of what this unknown dimension may be like.
Re: religion - yes, many are adamant that the Earth is unique in all the universe - if so much as a microbe were to be found elsewhere or to come from elsewhere it will jam a monkey wrench into things for them.
I would assume we'd have to depend on discovery of life on some piece of space debris after verifying that it didn't get transferred from within Earth's atmosphere. We lack the ability to explore even the closest planets outside of our own solar system due to the immense distances.
I'm an adamant atheist but admittedly the question of how life originated via abiogenesis is a sticky one. No one has been able to reproduce it so far. Then the question of how did it get from the simplest forms to vastly more complex forms. Think of the immense complexity of a human or even lower animals - the fact that anatomy grows the way it does with bones, marrow, cartilage at the joints, the spinal column, connective tissue, muscles, the vast network of nerves, the cardiovascular/circulatory system and various fluids within your body - saliva, mucous membranes, lubrication for your eyes, the balance of chemicals and hormones, the digestive system, the function of senses - and the nuances of what they can perceive - that you can generally tell where a sound is coming from in relation to your position even though you've just got two ears, DNA/RNA, and on and on - and that it's largely self-repairing, that one can become stronger and more skilled by challenging the body to work against greater stresses and repetitive practice, that your brain is structured in a way to control/process a lot of it along with immense storage capacity and other functions the brain is capable of - and that the blueprint for *all* of it is contained within the sperm and egg, including the capacity to participate in procreation yourself.
It's interesting how many commonalities we share with lower animals, and that there are things they can do that we can't. It's amazing that not only did life forms appear and evolve but the environment that provides sustenance also had to evolve as well.
To date human scientists can tell you what an amoeba is made of but they can't replicate an amoeba from scratch.
How did this all originate from the stuff of early Earth. Seems mind-boggling, yet there's evidence that suggests that's what happened.