It's called silencing.
Silencing is when rather than addressing the substance of whatever it is being talked about, someone tries to dismiss, trivialize or derail the conversation, so that the topic, whatever it is, stops getting discussed. The person who started the conversation ends up focusing not on the issue at hand, but on defending the validity either of the topic or of his or her own voice. Here are some categories of silencing, with specific examples from things that have been said to me or that I've heard said to others.
Suggesting you're being frivolous or the issue is not important.
"How can you waste your time talking about this when there are so many more important problems in the world?
"Shouldn't you be: a) spreading the gospel; b: helping the poor; c) taking care of your children instead of focusing on these issues?"
"The Bible is a toxic book riddled with errors and contradictions. Discussing what one of its verses means is a waste of time."
Questioning your motives.
"You're only talking about this because you want personal power/you're overly ambitious." (for an example, see Are Women Seeking Ministry "Demanding Rights"?)
"The reason you're saying all this is that in your heart you don't want to obey God."
"You're just trying to find a way out of following the Bible."
"What it comes down to is that you resent your God-given role as a woman."
"Deep in your heart you know there's no God; that's why you're arguing so much about it."
"Othering" you. ("Othering" is defined as "a way of defining and securing one’s own positive identity through the stigmatization of an 'other.'" In other words, "you're not one of us, so we don't have to listen to you.")
"You're not really an evangelical/you don't believe the Bible is inerrant [therefore, we can't trust anything you say]."
"You're one of those feminists, aren't you?"
"That's a bleeding-heart liberal response."
"That's a knee-jerk conservative response."
"What can you expect from a Christian?"
"This is all part of the homosexual agenda."
"No one who takes a different view on this position could really be saved."
Assuming you just don't understand, or you would agree with them.
"Sorry, sister, but you're deceived."
"Let me explain again why you're wrong, and maybe you'll get it this time."
"Try to consider this rationally."
"As any reasonable person could see. . . "
"Gaslighting" you. (The term "gaslighting" comes from the 1944 movie Gaslight, in which a young wife is manipulated by her husband into believing she is going insane. It now means any attempt by one person to make another doubt his or her perception of reality by "telling the other that there is something wrong with the way she sees the world or there's something wrong with who she is.")
"You're overreacting/too sensitive."
"You're getting emotional about this."
"I can see that you're bitter."
"You've clearly been a victim of abuse, so you can't look at this issue objectively."
"Someone in your past misused authority in a way that hurt you, and that's why you don't like hearing what I'm telling you."
Telling you to "lighten up" or "let it be."
"You're being strident."
"Why can't you just enjoy this sermon/movie/song for what it is? Why do you have to analyze it?"
"You're the one trying to silence us through insisting we be 'politically correct.'"
"Can't you take a joke?"
Privileging their position/appealing to authority.
"The Bible is very clear on this."
"The church has believed as I believe for 2000 years."
"But that's never happened to me."
"Most Christian women believe as I do and are happy."
"I'm a Greek scholar, and I know what I'm talking about."
Telling you to ignore the problem.
"It was a good sermon. If anything that was said bothers you, just forget that part."
"Don't be so negative. Do you always have to focus on that?"
"Just eat the meat and spit out the bones."
Telling you that the upset you're causing is more important than the problem you're pointing out.
"You're being divisive."
"Don't rock the boat/make waves."
"Stop making a fuss."
"Christians should be focusing on what unifies us, not on our differences."
Telling you that you talk too much about the issue.
"This is getting boring. Enough already."
"Stop beating a dead horse."
"Do you have to bring this up again?"
Anything sound familiar?
I'm pretty sure that almost everyone has had someone attempt to silence them, about something or other, at some time or other. But the point is that as soon as you start arguing with a silencer about whether or not you should say something, you've been effectively stopped from actually saying it.
I think we all need to learn to recognize these techniques, so that when someone attempts to silence us, we can simply point it out and then get back to the substance of the issue. And if we're responsible for attempting to silence someone else, we need to see that we're doing it and back off.
Issues need to be addressed on their own merits. Trying to shut someone up ultimately doesn't solve anything, and it's actually just another weapon in the arsenal of spiritual or verbal abuse.
The only words that need to stop are the silencing ones.
UPDATE: Dianna Anderson over at Faith and Feminism has written an amazing piece called White Lady Feminism, Christian Blogging and the Worst of Both Possible Worlds, where she provides an excellent example of how "Don't rock the boat" and "Let's only focus on the good things" are used to silence dissenters within a movement-- with a corollary of "We have to present a united front, so quit bashing your brothers!" which really should be considered as a silencing technique in and of itself.
Note: Saying "that's racist" or "that's sexist" or "that's homophobic" are not silencing techniques, because they do in fact address the conversation/topic of discussion, when the person saying this can point out how the prior remark is racist, etc. However, "You're a racist/sexist/homophobe" is a silencing technique because it's about the person making the remark rather than the remark itself.