I have given this issue quite a bit of thought and have had discussions with many other Stack Exchange users, some who are high-reputation and long time Meta Stack Overflow members, some who are community moderators on other sites, and some who are actually Stack Exchange employees.

It is my strong opinion that these posts should be dealt with as follows:

1. The posts should be downvoted heavily.
2. Constructive comments about why these posts are not welcome should be added. ("These answers are pseudo-science, this site expects answers backed by verifiable research", etc)
3. A "Citation Needed" post notification should be added. (Please do flag these answers and ask for a mod to do so)
4. The user should be warned via a private moderator message that their answers are attracting flags and downvotes, are low quality, and must be improved or their account may be answer-banned or suspended.
5. The answers should not be deleted by a moderator. If the author deletes the answer, this is an indication that they recanted and is acceptable (actually, desirable)

I know my view on this matter is extremely unpopular with many of the higher reputation members of this site. I do fully understand that as a community moderator it is my responsibility to act in the best interests of this community. As I am going against the popular onion of the highest reputation users of this community, please allow me to explain why I feel that I am not "ignoring" the community views and why I feel I am acting in the community's best interests.

First, let me make it clear that I do not feel these answers are valid and I do not feel the are good answers. That being said, I am a long time user of the Stack Exchange system (starting on Stack Overflow on March 9th, 2009) and I believe that the score of answers on stack exchange sites is the greatest strength of this system. I feel these answers are bad, but the negative score next to the answers shows that they are bad.

Left on the site, these negative score answers show that they are incorrect and not welcomed on our site. If these answers were deleted, the message that they are not welcome here is deleted also. Some have said that new users do not understand the score. To this I say new users need to learn what the scores mean early! If you don't understand what the score next to posts n a Stack Exchange site is, you're not a useful user. Post scores are at the very core of our system!

Also, these answers should have many comments explaining what is wrong as well as a "Citation Needed" notice. It should be abundantly clear what the negative score means. These answers *should also have a competing positive score answer. If these answers are left alone, then they do gain credibility and deletion should be seriously considered. But I think it is abundantly clear when these answers compete with good, positive score answers that they are incorrect and that his site is showing they are incorrect.

This sort of bad information exists. People believe it and people spread it. By deleting it from our site we lose control over it! if we instead keep it on our site, we gain power over the bad information and we can demonstrate that it 8is not correct*. Deleting the information makes it appear that we are somehow frighted by it, at least in my view.

The other major argument I have heard is that somehow these users posting bad information will accrue massive reputation and will somehow take over the site. I can't see this happening; if this were to happen we have a much more serious issue. If this is the concern than deleting the content is simply sweeping the problem under the rug.

Firstoff, these users should by far be the minority. The users posting good information should easily be able to overwhelm the bad users and downvote the answers into oblivion. The only users upvoting bad answers should be other bad users, which constitues a voting ring and is grounds for suspension and automatic vote reversal.

Second, there are lots of users on lots of Stack Exchange sites that upvote crap. there are sympathy upvotes, incorrect upvotes, etc. As a community we have to have the majority of users voting well so we can overrule the bad upvotes. This is the nature of the system.

Third, if these users continue to contribute nothing useful to the site, as I said in the bullets, they should be warned, suspended, and deleted. Therefore, they will rapidly lose any power and privileges they might have gained. As is, the user in question has a measly 24 reputation, and has already been warned to clean up her act or go play elsewhere.