The difference is, those are ideologies, not a single ideology.
And the vast majority of political ideologies in mainstream American politics constitute, together, an extremely anti-Marxist tendency. All mainstream political parties in the world's capitalist states operate so as to maintain the capitalist mode of production.
There are as many differences in opinion between Marxists as there are between apologists for capitalism and capitalists themselves; but the overriding ideologies of both are plain to see.
The US doesn't back any single ideology.
Sure it does: capitalism.
When a single ideology claims to solve everyone's problem, that's bullshit.
I'm interested where you're getting your assumptions from regarding all of this.
Neither Marx nor any of the serious Marxists after him claimed socialism would 'solve everyone's problem', whatever everyone's problem would be. It's not a utopian vision of society, it's a way of scientifically viewing and therefore critiquing society and therefore presenting a way to change it on the grounds of economic stability.
Fact is, neither religion, nor socialism have anything to show for on this entire planet.
Tell me what you're alluding to by 'socialism'. I hope it's not the state capitalist countries I've already informed you were never socialist in the first place...
Ideologies come down to laws. I'm assuming the one with the minimum set of laws must be more accommodating to everyone. Free competition or Capitalism is actually the least set of laws in an economic system. Again there's no laws against people who are willing to share with each other, but Marxism forces those who are not willing to share to do so. 