P.S. First, we love you. We need you. We must. We are ultimately giving you complete control over the creative products of our hearts and our minds.
Now, to business. It may be that other theater artists believe playwrights are just tapping into some unseen force and transcribing what we hear/see/experience ... basically, making shit up. We almost certainly are -- on the first draft.
Most often, however, by the time you get the script, we have left inspiration far behind. Playwrights know the muses are a fickle lot. We need them, so we court them and plead with them and bribe them. Unfortunately, once they show up, they don't want to leave.
They will drag us all over the wilderness, but if we let them, or worse, follow them, they never lead us to a good play. Is "never" too much of a generalization? I don't think so, but I'll soften the statement a little and say "almost never."
Muses launch plays. Reason and planning finish them. If the playwright has done the job, every word, every pause and every action is in the script for a reason. The article on the link at the top of this post points out that all the clues to your character is in the script somewhere -- by what is on the page and by what is left off the page. It also hints at the fact that some of the clues are in the lines other characters speak to your character, and the other way around.
Saying all the words and only the words is important for the play to work, but you know what? As a playwright, I don't care that much. I'll cuss you in my head, but I won't cry about any of it. You want to know why?
As much as we would like every performance to be perfect, playwrights (or reasonably intellegent playwrights anyway) know that isn't going to happen and we are kind of ok with this fact because the play can be done again somewhere by different people with different failures. The play is actually a living thing (which makes it so much more appealing to me than film). You may screw our intent for the run by dancing fast and loose with the text, but the play will survive despite you. Just as it will thrive with you.
So, don't stick to the script for the playwright. Stick to the script for your fellow actors. If you don't say a line the way the line needs to be said -- for whatever reason -- you are shafting at least one person on that stage and more likely two or three or all of them, because if the play is written correctly everything is linked to everything else to some degree.
Basically, your added "um" or switched-up lines may be easier for you to remember or say, but every action has a reaction and the butterfly of your errant "um" can set in motion a hurricane of cause and effect that changes the way, for instance, your love interest feels about you by the end of the play. In a delicately written piece, the love they feel for you may actually only be held together by a thread. Break that thread with an inappropriate pause, sour glance, rushed moment or over-indulgent bit of lazy filler and the whole thing can fly apart.
Unfortunately, the character has to stay in love with your character because it is in the script. And the actor playing your love interest has to find a reason for the character to remain in love no matter what the hurricane you created dictates. That isn't always, or even often, possible.
End result? Congratulations! You have just shafted your partners. Shame on you.
If your errant "um" or switched line doesn't at least subtly change the whole play, though, shame on the playwright. He hasn't done his job.