I am putting the Psalms to the music of popular hymns using a software called MuseScore. I noticed that many hymns start with an anacrusis and then divide the measure at the end of the line,so that the line ends at the end of the sentence/thought. I am wondering if I can leave out the anacrusis and just start the song on the first beat of the first measure. This makes it so that the last beat of a line is also the last word and avoids hyphenated words on two different lines. My specific question is: are anacruses necessary or a preference? Will eliminating them change the music?
It really depends on the text. If the psalm that your trying to set needs the anacrusis, then you'll have to leave it in. If you can start on without it, then you can leave it out and adjust the music accordingly.
And yes, it does affect the music. In setting text to music, you need to think about prosody which is how the words are emphasized using the music. Typically, people try achieve as "natural" a prosody as possible - that which most closely resembles human speech. Other composers do the opposite for a very specific effect. Considering that your goal is likely for these psalms to be sung by a congregation of lay people, it would probably be in your interest to make the words fit the music as naturally as possible.
I would study each psalm, then pick a hymn tune that seems to match the words pretty well (the least amount of effort / changing on your part) and then adjust the music as necessary to fit the words. Again, leave the anacrusis if it fits the text; take it out and adjust if it doesn't.
Anacruses are there because there is/are syllables/words that need to come before the first emphasised word. By leaving them out, the first line probably won't make much sense, and that then puts emphasis (in the form of first word in a bar) in a different place.
Think of 'Happy Birthday'. The anacrusis 'happy' is there so the emphasis is on 'birthday'. Remove that altogether, or start the bar on 'happy' and the song is changed throughout.
To add to Tim's answer the phrasing will also be wonky. If you for argument's sake have 8 bar phrases and let's say a minim upbeat in 4/4 time then the phrase will end on the second beat of the seventh bar.
If you omit the upbeat then there will still be this pause in the music in the middle of bar seventh, but this unusual division of phrases.
Then you will have to change the phrase structure, but at that stage, you are changing the song to such an extent that it would be easier to just make a new adaptation of the song.