Is it worth getting into political arguments on Facebook? Will it achieve anything but aggravation?

The only time it would be worth refering to politics on Facebook is if you are actually looking for a heated argument.  It is near impossible to have an unbiased, objective discussion on FB regarding politics.  When most attempt discussing politics, the discussion quickly becomes personal and derogatory.  Pointing fingers and referencing past events with little factual data is what you're likely to encounter.  For these reasons I do not discuss politics on FB anymore.  I use to get so irritated on FB when attempting to have a political discussion that I just completely stopped engaging with others.  You can find pages to follow as well as groups that are tailored toward your idealogical preference, but don't expect to find an area that is specifically geared toward objective discussion.  FB is tailored for satisfying individuals quickly and personally.  I have found that many individuals on Google Plus have left FB for these reasons as well.

I'd say block her posts from your news feed, and de-friend her when you or she move(s) away.

Total waste of time to argue on the internet ...

No because often we only hear or see the variables that fit our ideology and discredit those that contradict it.  One option, is to simply hide all posts from your friend.

I would not get into an arguement with her. Just tell her that you want to leave the politics and those types of issues out of the friendship. If she then won't stop, then block her. She will either be respectful to you and the friendship or she can get the hell on somewhere else.

I believe Facebook is too public a forum to, "get into it."  I think most people challenged in that fashion would, almost by reflex, retrench and harden their views.   If this person is truly a friend, and the matter is that important to you, probably the best - only? - way is to have a conversation, ideally face-to-face.   Then, you might or might not want to reconsider your FB "de-friending" options.

There is a good video by WSAZ TV on how to deal with political discord on Social Media here: http://www.wsaz.com/content/news/Dealing-with-political-discord-on-social-media-368273801.html They suggest one way to avoid arguments or fights on Social Media is to use filtering mechanisms to filter out contentious content.

Like they say never argue with idiots they will bring you down to their level and beat you at it. If it ends up becoming inconclusive then obviously it's not worth it but if there is a huge group arguing then sometimes it is fascinating to see what people come up with. Be it in the form of conspiracy, vote-bank politics or how can one change their own notions. And social network is the future of democracy be it in the selection of electorate or initiation of a reform.

One of the upsides of the internet is in building small niche communities of people that are geographically diverse but share the same interests.  One of the downsides, is that narrow-minded viewpoints can be selectively re-inforced since you can choose to interact only with people who agree with you, and never have to tolerate dissenting opinions from your community.  If no one challenges her radical views, she will assume such views are reasonable and accepted by her peers. You may not be able to change her opinions, but at least you can point out that her views are offensive to many people and might get her to soften her language.