Homeopathyphile or homeopathophile, a neologism, alas
homeopathy, definition from Merriam-Webster
a system of medical practice that treats a disease especially by the
administration of minute doses of a remedy that would in larger
amounts produce in healthy persons symptoms similar to those of the
homeopathy etymology, from Etomonline
1830, from German Homöopathie, coined 1824 by German physician Samuel
Friedrich Hahnemann (1755-1843) from Greek homoios "like, similar, of
the same kind" (see homeo-) + -patheia "disease," also "feeling,
emotion" (see -pathy). Greek homoiopathes meant "having like feelings
or affections, sympathetic."
We all know that -phile is Greek (see Dictionary.com):
a combining form meaning “lover of,” “enthusiast for” that specified
by the initial element: [example] Anglophile
Thus, we get homeopathyphile, which, when entered into the Oxford English Dictionary, returns:
No dictionary entries found for ‘homeopathyphile’
Nor does the OED recognize homeopathophile.
Searching further, I found a reference on Twitter:
A patient was blown away by what a homeopathic remedy could do...And
so, a homeopathyphile was born
The OP hoped there was a term that was not derogatory, and I manufactured one for him with three Greek roots -- impeccable etymology. Maybe it will emerge from the twitterverse into mainstream English.
Addendum: Thanks to @Peter A. Schneider for the alternate homeopathophile.