Then I noticed that coconut oil is a good source of lauric and
caprylic acids which minimize Candida growth.

Two facts:

1) Most of your CMI is around your gut.

Blood cells responsible for Cell Mediated Immunity (CMI) exist largely
in lymph nodes.  Most of the lymph nodes in your body are Gut
Assocated Lymph Tissue (GALT).  I assume that the reason for this is
that the food you push through your gut carries a high every-day
infection risk so you better position your defenses where the
infections are happening the most often.

2) Activated CD4 T-cells are the breeding ground for HIV.

Resting CD4 T-cells are only latently infected.

<< Early establishment of a pool of latently infected, resting CD4(+)
T cells during primary HIV-1 infection.

Chun TW, Engel D, Berrey MM, Shea T, Corey L, Fauci AS.

Laboratory of Immunoregulation, National Institute of Allergy and
Infectious Diseases, National Institutes of Health, Bethesda, MD
20892, USA. twchun@nih.gov

The presence of latently infected, resting CD4(+) T cells carrying
replication-competent HIV-1 has been demonstrated in chronically
infected individuals who are antiretroviral therapy naive as well as
in those who are receiving highly active antiretroviral therapy
(HAART). [...snip...] >>

Put 1 and 2 together and the big picture is that the gut is the main
source of HIV due to a constant onslaught of infection from even very
minor food poisoning, the kind a person without an HIV infect just
repells without even noticing due to their CMI.  The HIV infected
person's CMI being activated by a constant source of infection like
persistant Candidiasis right up against the GALT is where most of the
latently infected, resting CD4(+) T cells go active and release HIV.

Anything that stops persistant Candidiasis will most likely reduce HIV
viral load too.