At our parish when the psalm is sung, the text used routinely varies from my new and authorized prayer book. Is it acceptable for the musicians to change the words as they do?

No, if that is what they are doing. The proper responsorial Psalm, from the day should be said or sung, however there are exceptions. Liturgical norms state the following: 
 
[T]he responsorial Psalm, ... should, as a rule, be taken from the Lectionary. It is preferable that the responsorial Psalm be sung … In order, however, that the people may be able to sing the Psalm response more readily… Psalms… chosen for the various seasons of the year… may be used in place of the text corresponding to the reading whenever the Psalm is sung. If the Psalm cannot be sung, then it should be recited…. There may [alternately] be sung either the Responsorial Gradual from the Graduale Romanum, or … Graduale Simplex…or an antiphon and Psalm from another collection … providing that they have been approved by the Conference of Bishops or the Diocesan Bishop. Songs or hymns may not be used in place of the Responsorial Psalm (GIRM # 61) 
 
As can be seen, an exception can be made for reasons stated to using the psalm for the day. In some parishes, the ability of the musicians and or the people to learn and use different responses each week varies a good bit. Thus pastoral provision permits the use of certain seasonal psalms and refrains. But, substituting hymns in place of the responsorial Psalm is not permitted and only texts approved by the Bishops are to be used. 
 
Thus it is possible to see how the words of the psalm that are sung may differ from what is in your prayer book, but only if the variant text is approved by the Bishops. 
 
For musicians, parishes or pastors to make unauthorized changes to the texts of the psalm is strictly prohibited. Most commonly the forbidden changes involve altering the text to be “inclusive.” But theologically, the “Man who walks not in the counsel of the wicked” etc., is often a reference to Christ, and altering the text loses the Messianic reference. Hence bad and unauthorized changes yield bad theology. It is rightly prohibited.