Evolution is certainly regarded as a scientific truth by tons and tons of scientific bodies. The National Academy of Sciences summed it up as follows;
"Scientists most often use the word "fact" to describe an observation. But scientists can also use fact to mean something that has been tested or observed so many times that there is no longer a compelling reason to keep testing or looking for examples. The occurrence of evolution in this sense is a fact. Scientists no longer question whether descent with modification occurred because the evidence supporting the idea is so strong."
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Also, your critisism of our lack of an explanation for abiogenesis is not a critisism of evolution. Evolution describes what has happened once life was started. Abiogenesis is something entirely different, much like plate techtonics describes how the earth's crust moves, but doesn't tell you how the Earth formed in the first place. I'm not sure what you're referring to regarding modern speciation or the discontent of some with "Origin of Species".
As far as the big bang goes, there is some wiggle room there. Steady state has become obsolete, but inflation (multiverse) and others are interesting possibilities, but don't have as much evidence supporting them now as does the big bang. My guess is someday there will be something that replaces the big bang, but that's just my opinion. However, when you view Carson's comments, it's clear his quibble with the Big Bang isn't a scientific quibble, it's a religious one, and that's something you'd have to address to address his comments specifically. He wasn't up there giving a presentation on the multiverse theory. He was preaching.
Regarding the Muslim stuff, I would ask this. Should hard-core fundamentalist Christians be excluded from public office? There are some that think the laws of the old testament are God's law and should still be obeyed. The killing of gays, the stoning of adulterors, you know, all the Leviticus and Deuteronomy stuff. Just as you have liberal and moderate Christians that wouldn't seek to impose their beliefs on the nation, there too exist liberal and moderate Muslims that wouldn't try to install Sharia Law. After all, any person taking oath swearing to uphold the Constitution deserves the chance to do so, right? Or should we assume any and every Muslim would break that oath?