Religion has taken up camp in the right wing of American politics. Somewhere along the way, the Right wing became the religious zealout wing. This was not always the case. At any rate, the right wing has aligned itself with the church and their beliefs. Because the power of one side of the coin that is the dual party system we have in the US is largely religion affiliated, science that counters religious claims are labeled as heresy and not allowed to be taught in pulbic schools.
It's because of religion that people question things like the age of the earth, whether climate change is actually happening, and if evolution is a fact. These three things are, of course, factually known by science, yet religion creates a certain ignorance that makes people question these simple and well-known facts.
No, scientific advancement in the United States is not hindered by religion, because the religious people who disapprove of science are few and far between. Most Christians, and people of other religions in the United States, believe in science and want to further the advancement of science and the possibilities that it offers.
We have so much freedom here from religion that as long as an act isn't against the law or completely immoral, scientists have the right to do it despite some people's belief. In other countries it may be different because of the government, but here the government is the people and religion is seperate from the state.
I do not believe scientific advancement in the United States is the least bit hindered by religion. I believe scientific research goes on without being hindered even if it has to take place outside of the United States. I'm sure that many advancements arising from research facilities do not make newspaper headlines, but are quietly celebrated and eased into the mainstream.