Defintely don't wear anything you don't *have* to wear in these conditions.
A good primer definitely helps. For humid days I usualy go for Hourglass Veil (way pricey but I like to indulge in its luxury every now and then) or CoverFx Mattifying Primer. I was putting a lot of effort into testing every primer I could for a while and these, for me at least, were the best performers for humidity and sweat.
On top of that I'd wear the sheerest foundation you can get away with. Use concealer sparingly. Avoid heavy product application especially in areas that sweat a lot of have larger pores. Both of these will tend to disrupt anything layered on top of them.
You might think that skincare wouldn't be such a concern in high humidity conditions, but if your makeup starts deteriorating it will become especially uneven over areas of dry or unhealthy skin. In my opinion good skincare is actually the #1 secret to flawless makeup.