male vegan conspiracy theorist here. Perhaps I can offer a viewpoint from the other side of the fence, as it were?
I notice your thread is earmarked as conflict aversion. The best way to avoid a conflict, is not to seek a fight in the first place. You appear to be assuming your friend is wrong based on their beliefs, but you haven't mentioned asking them for any evidence or considering why they believe what they do.
Contrary to all the hostile opinions here, conspiracy theorists are not an irrational bunch. For example, people here are advocating using empathy as a solution to try to prove someone wrong, in response to your question, but I don't think that's a particularly empathic thing to do, and if I had read a close friend was trying to be empathic to me only in an effort to undermine my beliefs, I wouldn't consider them as a friend.
Allow me to contrast; when I meet people, the first thing I do is try to find common ground with them, and I don't try to start arguments or try to prove myself right (because a friendship involves overlooking differences).
I see a few other suggestions and views here that I'd like to comment as to why they wouldn't work, or aren't valid. You say that:
In my opinion she is not nourishing her body properly
Are you a professional dietician, or is this just purely your opinion? If you're trying to prove her wrong over an opinion and not a substantiated fact, you're not going to get anywhere on this point. On another:
even when she gets a prescription, she wouldn't always take the meds
Medication does carry side-effects, and as a vegan, I can also comment a lot of medicine also contains animal byproducts, which would very likely explain why she refuses to take the meds as a vegan. The fact you say she "wouldn't always" implies that she does "sometimes". It's curious why you haven't considered this possibility and seem to have framed it as her distrusting the meds (if she distrusts all meds, she wouldn't take any).
Personally, her private medical affairs are hers, between her and her doctor or appropriate physician, and as you haven't expressed having any particular medical training, isn't really something you should be trying to 'correct' her on (a lot of people might try to avoid acknowledging an allergy, for example).
You also mention:
I hate that I hide my chocolate & pretend to be vegan in front of her to avoid upsetting her.
Have you told her this? Did you ever tell her (falsely?) that you were a vegan, or are you merely hiding being a non-vegan?
If she values your friendship, she will be courteous to you, and let you eat whatever you want. As a vegan myself, I thoroughly understand other people have differences of opinion, and so long as they're not trying to cover me in geasy meat laden hands, I don't judge what other people eat.
On the other side of that fence, it is also possible to get vegan chocolate (usually sold in ironically named health shops). But I feel you need to let her know her preaching is hurting the friendship.
I notice another poster remarks:
Consider introducing her to proper studies, research papers and the process they go through before its accepted by the scientific community
According to the British Medical Journal there's issues of publication bias, such as companies only publishing trials that present products in a favourable light (and hiding trials that show adverse effects), or as mentioned, even outright fabricating evidence or data. It isn't helped by the fact that nonsense papers regularly get accepted (there's even a tool that generates them online).
So in a sense, presenting one set of scientific study to refute another, when the process has had a lot of questions raised (both in the past and recently), is a no-win scenario. Presenting scientific studies is merely just going to add more fuel to the argument fire.
Unless you're prepared to hash out a sensible, level-headed debate (and when it comes to passionate opinions, no-one behaves sensibly), there's nothing to be gained from this.
Another poster remarks:
anti-vaxxers rely on ignoring accepted scientific consensus and evidence etc.
Science isn't a democracy, and isn't based on a 'consensus' (Galileo, for example, was extremely unpopular), it's based on facts. It would be a sad day for exploration if scientists merely socially agreed, and didn't seek to push boundaries (if anything, cutting edge discoveries like Higgs-Boson are founded on disagreements and people conducting experiments to prove or disprove a hypothesis).
But these presumed stereotypes don't help. Perhaps she's seen the US vaccine court or VAERS (Vaccine Adverse Event Reporting System), or the long list of side effects that is documented with given vaccines. Personally, I'd argue her aversion is much more simple; vaccines contain animal products, and this is a possibility no-one seems to have considered.
Specifically, depending on which vaccine, they can either contain virus grown in cultured cells of egg (animal product), or they can make use of dead fetus cells for virus growth, which whilst human, would definitely violate all bar the most hypocritical of vegans' beliefs.
It's my strong opinion that a large portion of the behaviors are attributable to veganism, and the others are arguably non-issues (for example, nutrition and health both require specialist knowledge, and unless she's trying to force you to no get a vaccine, her other beliefs should be irrelevant in day to day friendship).
I think you need to tell her, if she is indeed preaching (I assume this is the case, however the way you've written it comes off as you've observed her behaving this way and seek to 'correct' it, rather than embracing the diversity), you need to tell her, her attitudes towards you, are hurting you/harming the friendship, and propose what you're after, like 'I want to be able to eat non-vegan foods without worrying about you criticising me on this'.
I can tell you from experience, you either prove yourself right (that of course assumes you are right), or have a friendship, but you often cannot have both. The process of disagreement is anti-thetical to friendship (the latter is common ground; what do you have in common with them?).
You say you like their friendship, so how about encouraging the parts you like?
If you really want to prove them wrong, however, you need to examine what their argument rests on. What evidence or reasons do they use. Then you have to impartially dismantle it. Truth is, arguments which are right, can be presented weakly (a strawman argument), both your own and theirs, and likewise, arguments which are wrong, can be made to seem strong (publication bias, hiding of averse data etc).
I think you need to choose, do you really want to prove them wrong, or are you a friend that looks past differences?
[Apologies for the length, but there's been plenty of answers on the other side. I won't be surprised if I get downvotes, but IPS involves considering all sides, and I felt the need to hypothetically present 'hers'.]