Different religious beliefs by Americans definitely helped shaped opinions on hot button issues like abortion, euthanasia, and gay marriage during the 1990s. The 1990s saw a significant number of evangelical Christians carry on the political agendas of organizations like the Moral Majority from the 70s and 80s. This included a clear stance against abortion, euthanasia, and gay marriage. However, many mainline Christian denominations made a more liberal turn where they became increasingly more open to things like gay marriage as seen in the many churches that adopted polices allowing gay ministers.
Another aspect to consider is the affects postmodernism has had on religious beliefs in America. After the collapse of the Soviet Union and subsequent end of the Cold War, and after racial and ethnic genocides in the Balkans and Africa, many people in the West began to openly question modernist notions of reality just like after the two World Wars. Many religious and nonreligious people alike became uncomfortable with claims to absolute truth or certainty. They saw the absolutist claims of Hitler, Stalin, Slobodan Milosevic, fanatical Muslim terrorists, and even televangelists as dangerous to society. Postmodernism begs the questions of what is truth and how can we know it along with if an individual claims to know truth, how can we know that he or she really does know the truth?
As a result of the explosion of postmodernism in America during the 90s, people of all faiths, as well as the irreligious, have begun to question foundational beliefs and doctrines with fresh perspectives and a more skeptical outlook. The results were as different as the number of faiths in American society. For some, postmodernism led them away from their faith in any type of official religion to a more individualized form where they ultimately decide what they think is truth. For these people any hint of someone or some institution trying to tell them what is truth is seen as an invasion of privacy and disrespectful to their freedom of choice. For others, postmodernism strengthened their faith as they shed some old assumptions and embraced their faith in new and exciting ways. Rather than feeling threatened by other religions, many of these people were more open to working with people of different faiths. Others, like fundamentalists of different religions, saw postmodernism as a threat to the belief in absolute truth itself and dug in their heels more in order to protect their faith's truth claims.
Religion has always affected the average American, but American religions like all others are not static sets of beliefs that are practiced the exact same way over long periods of time. No, religions change with the changes of society and the postmodern affects during the 1990s on American religion can clearly be seen today.
This is surely an impossible question to answer in any really accurate way. During the 1990s, much as it is today, American society was made up of people who were affected by religion in a variety of ways. There were everything from militant athiests to zealous religious fundamentalists.
During the 1990s, as now, the vast majority of Americans said that they believed in God. A large minority actually attended religious services on a regular basis. Then, as now, some of the most important cultural/political issues revolved around religion and morality. The most obvious of these issues were abortion and gay rights. The push to impeach President Clinton was driven to some extent by religious attitudes towards sex. However, given that 95% of the country professed belief in God, it is clear that people's mindsets on these issues were not all affected by religion in the same way.
During the 1990s, as now, the majority of Americans believed in God. However, the degree to which this belief affect their mindsets cannot be generalized.