What is the importance of religious tolerance?

This is an important question, but I really don't like the use of the term "tolerance" in this context.  We use this word to indicate that there is something we do not like, but we are putting up with it, as I might say a teacher tolerated students' misbehavior.  What I do think we want to promote is understanding and respect for other religions.  And this is crucial to getting along in the world today if only because there are different religions, deeply held personal and societal beliefs that people should be permitted to hold in peace.  These beliefs may be similar to or different from our own, but those different can offer us new perspectives, and those similar can help us find common ground with others.  In order to live peacefully in society and to expand one's horizons, other religions should be respected.  This does not mean that we have to agree with another religion's point of view, but it does mean that we should learn about them and at the very least, agree to allow people to hold their beliefs without interference.
What happens when we do not have religious tolerance, much less respect? We have the Crusades.  We have the Islamic State.  We have someone knifing an imam and the beheading of Christians. We have the Holocaust.  Sadly, while these examples may seem extreme, they are the logical consequence of religious intolerance.  If we call America a Christian nation, we are lacking respect for all the Jews, Muslims, Hindus, Sikhs, and others who form our country, which sets citizen against citizen and which relegates other religions to a lesser status.  When the French ban burkinis, the message they are sending is one of intolerance for religious beliefs, sadly, in response to the intolerance of a group of terrorists for the religious beliefs of others. 
Religious beliefs are not meant to be rational.  They are simply beliefs, lacking in evidence and coming from our hearts. We do not want our own religious beliefs to be attacked.  We want to be able to observe our own religions in peace.  To deny someone else the ability to worship without criticism or attack when we find it so distasteful for ourselves to be thus denied seems completely unreasonable.  To do so causes dissension. To do so causes strife. To do so causes wars and genocides.  If we seek to worship in our own ways, it is not rational to prevent others from doing so.  And that surely is the point of religious tolerance, tolerance being the least we should strive for. Even better is to learn, to understand, and to appreciate the differences, all the fascinating spiritual paths that people follow.