The findings come from "The State of Free Speech and Tolerance in America" survey by Washington DC based think tank the Cato Institute.
The poll also went a step further and asked what should happen to a religious baker who refuses to bake a special-order cake for a same-sex wedding.
Most Americans (66 per cent) said nothing should happen to the baker.
However, 20 per cent of people surveyed said they would support a boycott of the bakery and 22 per cent would agree with a government punishment including: issuing a fine, requiring an apology, issuing a warning, revoking their business license, or sending the baker to jail.
Another 6 per cent support suing the baker for damages.
However, the report showed a split in public opinions about serving LGBT people vs. servicing same-sex weddings.
Fifty per cent said businesses with religious views should provide services to homosexuals. However, only 32 per cent said a baker should be required to bake a special-order cake for a same-sex wedding.
The findings come after a Christian cake artist from Colorado refused to make a wedding cake for a same-sex ceremony.
Jack Phillips, owner of Masterpiece Cakeshop lost a case in 2014 in Colorado Civil Court. His legal battle has been taken to the US Supreme Court.
Also, Ashers Bakery in Northern Ireland has taken its case to the UK Supreme Court after it was accused of breaching equality laws by refusing to make a cake which supported same-sex marriage.
