Could A Different Sperm from Dad Hitting Mom's Egg, Still Make "You"?

Possibly with different features like eye color but still the same "self", "consciousness," "soul" or whatever you want to call it. Or did you need that exact sperm/egg combination to ever exist?

Seems like how you and others would answer this question has become relevant nowadays. Would more religious people than atheists answer "yes"? Would more Republicans than Democrats?