Do religious beliefs give people the right to force others to follow these same beliefs?

No,

it's one of the dangers of religion, it shuts down peoples rational thinking.

NO!!! But Christians insist that that's how the American government is supposed to work.

For example, America is supposed to have no slavery, but Christians want women to be slaves to a fertilized egg.

Another example: States are supposed to have equal protection under the law for all persons within their borders, but Christians want to return to the old days of segregation - starting with homosexuals. SEPARATE IS NOT EQUAL.

If God hates abortions, I want to hear it from him directly, at which point I will ask why he wrote an entire chapter in the Bible where he told Moses how to force a woman to have an abortion against her will.

No.....because the true God gave man free will, the right to choose. If any religion forces their beliefs on others they are going against God.

No. But across the ages many Christians have been put to death by horrible means such as burning by other Christians who were trying to force them to worship God in a particular way.

This is what happens when people redefine a word: confusion. Nobody is forcing anything here. You live in a free country, where one vote counts as much as the next.

If a religion has the law "do not kill" then any laws they have that encourage killing someone cannot be carried out because they will be breaking this law.

The law "not to kill" and the law that says "to kill" causes conflict because one cannot be carried out without conflicting with the other.

The Romans had no problem converting people to their official religion, Christianity, by sword.

So yes is the answer to your question!

The religious believe they are ordained by god to kill any who disagree with their religion.

higher purpose always involves misery or endurance for a common goal

hell (metaphorically speaking) NO!