There are a few distinct differences between that older bills and this new one, even though the title is somewhat similar.
First, the law applies to for-profit businesses. And religious beliefs can be used as a defense in any private lawsuit. This clause was added because a similar New Mexico law lost a legal challenge for those reasons. The federal law does not have this clause. The original federal law and most of the state laws that copied it, are based upon keeping the government from interfering with expression of religious views (like muslim inmates being allowed to keep beards).
NExt, the law applies to protections of practices whether or not compelled by a system of religious belief. That is, very fringe practices not justified by the religion are under the protection here. So even if your church has no divinely inspired scriptures telling you to not sell products to gay people, you can still claim that you are protected by this law. Thus the Church of Cannabis has opened in Indiana, with the use of cannabis being a part of their beliefs, using this law as their basis to exist legally.
The federal law at the time was a relatively benign law, meant to protect things like feeding the homeless in parks. Since then the law has been interpreted differently by several courts and many of the people originally supporting the law in congress have backed away from it. Having a similar title does not make two laws the same thing.