The same is true of a non-Mason reading Masonic materials. Some don't understand the historic source of the terms used in Freemasonry. This is simply a matter of misunderstanding. The leader of the Lodge is called the Master of the Lodge for the same reason the leader of the first violins in an orchestra is called the Concertmaster, or a highly skilled electrician is called a Master Electrician, or the leader of a Scout Troop is called a Scoutmaster. Masonic use of the term Master originated in the guilds of the Middle Ages when the person most skillful was called the Master.
Much Masonic vocabulary dates from that period.
Worshipful John Doe means exactly the same thing as the Honorable John Doe. There is certainly nothing irreligious in the title as used in Masonry. There is nothing offensive in Masonic rituals, at least not to anyone who understands them. They are ancient, many of them so old their origins are long lost in history. But there is nothing bad in that.