What should I say to people who accuse me of believing in a "Pixie in the sky" and fairy tales because I believe in God and ask me for proof that He exists? (Or do I just ignore them?) I feel like I should say something, but it's quite hard to say anything that will convince someone who starts out with these views, as they usually get ruder with each attempted defence and I don't have your gift of making sense of everything.
My absolute honest answer is to run, run as fast as you can and don't look back lest you turn into a pillar of salt. At the point where someone is accusing you of sprinkling pixie dust, nothing you can say will convince them otherwise. The truth is that the entire reason they want to engage you at all in this discussion is to belittle you. You may as well dance a hulu and sing "Here Comes Santa Claus" as try and testify to your faith.
Unfortunately for you, (and me) Jesus would prefer that we didn't do this. He didn't do it to the point where He was crucified for not shutting up. He could have just shut up. He chose not to duck out.
Here is the tactic I employ. I try not to answer right away. I ask them what they believe. Everyone believes in something that is unseen. Love, for example.
"Do you believe in love?"
"Yes, of course."
"How do you prove it really exists? Neurologists say that emotions are complex neurological states in the brain that motivate us to act."
"You can show love, in how you behave toward another person."
"That is absolutely true. Although....once in a while we find people who we believe love us because of what they say and how they behave toward us, only to be betrayed by them, or hurt by them, or beaten up by them, or murdered by them. How do we know when love is true? How can you tell when love is real?"
"Well...you just...you can..."
"Tell that to my friend Ruth who just got dumped by her boyfriend of three years. Love exists. But it can't be proved, except through time. The answer about love is that you just have to take the risk, take the leap of faith to experience it or stay alone and lonely."
"That has nothing to do with a big man with a beard in the sky who makes up rules and sends floods to bad people."
"I think it does. But I'm not that smart. I like to read what actual smart people have to say. Like Einstein. He's the smartest person I can think of. He recognized the impossibility of a non-created universe. Einstein believed that God reveals Himself in the harmony of what exists, which actually is what motivated Einstein's interest in science. He once said, "I want to know how God created this world, I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts, the rest are details." He also said, "Science without religion is lame, religion without science is blind." So, if you want to argue with someone, go argue with Einstein. And good luck with that."
The truth is you are not going to be able to make sense of everything. But neither are they. If they try to explain how the world works, they are going to have the same difficulties you do. No God? No afterlife. I'll bet they believe in ghosts, though. Most people do. How do they explain that, besides admitting their own cognitive dissonance?
In the end, it may be the best you can do to say, "I have not been rude or belittled you for your beliefs. I cannot prove to you that God exists anymore than you can prove that He does not, so I'll thank you to give me the same respect I have given you."
Make sure you have indeed done that. All people are God's creation. Even the rude ones.