I have expressed myself elsewhere about the pros & cons of songbooks in general & RUS in particular at sings. Here I will suggest some ways to make books less obtrusive & possibly easier to tolerate.

Reading is faster than singing, and most of the time, in addition, you will have sung or at least heard the song before. Using a crib to sing is not like reading aloud from a newspaper. When I am using a book I try to confine myself to occasional glances, and face the company the rest of the time. A quick scan in advance, to see if the version you know is different, may also be advisable.

All that is all the easier if you are sitting around a large, well-lighted table. The book is horizontal, you don't have to hold it, and your nose is not in it. (Also, your drink is handy.) That used to be the standard setting for convivial singing, and Don Duncan provided it for his sings at Old Joe Clark's of blessed memory. It limits the size of the company, but that is fine with me.