Are downvotes and closing questions rude?
No, downvotes and closing questions (as well as upvotes and reopening questions) help us sort out quality content and enforce the quality standards laid out in the FAQ. People don't like downvotes, they don't like having questions closed, but these actions are vital to the survival of our site. By closing unanswerable, off topic or discussion questions we keep the bar of quality on this site high. We are in beta, and beta sites can be shut down for low quality.
Do not be afraid to vote to close questions or downvote low quality questions; if you can't vote to close, flag the post. We will not be lowering our quality standards. Our standards can be hard to grasp when people first find the start, and they're a lot higher than other sites out there on the web. This is because we don't want to be just another site out there on the web. Ignoring the risk of being shut down, making this site a high quality resource should be our goal; I became a moderator to help this site along in that regard.
I think Jeff Atwood put it very well here:
not everyone can attend Harvard. Or even the local community college. Stack Exchange has the rules it has about questions and answers because that’s what makes us Stack Exchange and not, y’know … Yahoo Answers or Reddit. Anyway, my point is that when people say "you guys are mean!" they often aren't actually talking about civility at all. They just want Harvard to let them in and/or loosen their requirements for applicants. Of course, doing that would make Harvard.. no longer Harvard. Please do not conflate these two very different things.
Is disagreeing rude?
It's perfectly fine to tell someone "don't do that" in a comment or answer. If someone is asking how to accomplish a goal that is professional suicide or otherwise dangerous, that's exactly what answers are for. Share why they shouldn't do whatever they have said; a quick "I don't think you should do that" is not an answer. Answers should always explain why you're giving the advice you are so we can evaluate their accuracy.
Just because you aren't saying what the asker/other people want to hear doesn't mean you're being rude. Don't be afraid to give an answer that disagrees with other answers, just be civil, as you would in all other answers.
What exactly is rude?
Being rude is being a jerk. It's saying "You're stupid to do that" instead of "You shouldn't do that". It's saying "Your post sucks" instead of downvoting and moving on. It's not just saying something people disagree with, it's doing it in a way to be intentionally or dismissively mean.
Using the primary functions of the site as intended (voting, answering) is never "rude". What can be rude is how you express yourself in your questions, comments and answers.
When a question is closed or about to be closed, the asker might be upset. It's not very fun. Do leave guiding comments saying why the post isn't acceptable and how it can be improved. Just be civil and focused when making those comments; if all you say is "this is off topic" or "please read the FAQ" well, the close reason already says that.
Don't belittle people, call them names or attack people. If you see a post that is rude, go ahead and flag it as "rude/offensive"; a moderator can edit out the rudeness or delete the post/comment. In the case of repeat offenses a user may be suspended for repeated, abusively rude behavior. If the rudeness is minor and in a question/answer you can go ahead and edit it out.
There's also another fabulous guide on rude comments on Arqade's meta.