Q. Is it right for people leave their Siddur open after a service?
A. Definitely not. One should not walk away leaving a holy book open, even upside down (Shulchan Aruch, Yoreh De’ah 277). It is an insult to the book, like walking away from a person while they are still talking to you (Minhagei Y’shurun, p.103).
Further, if the book is left open something might fall on the open page and make it dirty.
Some say there is an angel called Shed, the initials of Shomer Dappin – “he who guards the pages”. He shows his displeasure with a person who leaves a holy book open by causing them to forget their knowledge! (Shach to Yoreh De’ah 277).