Sorry - there is no "beating the humidity," only accepting it and carrying on lol!
Accept... that the pavement will be damp. Your clothes will be damp. Your hair will be damp. The very air will be damp.
Accept... that high humidity means that sweat doesn't evaporate well. And when sweat doesn't evaporate well, things happen. Things like clothes getting very, very wet - you want technical, wicking fabric not because it wicks the sweat away and makes you dry (it doesn't), but because it doesn't hold water very well, so it doesn't get heavy and uncomfortable.
Accept... that when sweat isn't evaporating due to high humidity, AND the air is warm/hot, the greater is the likelihood of overheating. SLOW down to compensate.
Accept... that if it's hot and humid and sweating buckets, you should be hydrating, but you're also losing electrolytes, so have a plan for replacement, be it on-course Powerade or BYO item of choice.
Personally, I never chafe in high humidity because my skin stays slick from sweat and glides instead of sticking. But I hear plenty of folks say they do chafe in humidity, so best have a plan for that. Body Glide anywhere clothes could rub skin (underarm seams, bra bands, waistbands, etc.), and places where skin rubs on skin (inner thighs, underarms, etc.)
Also, SUNSCREEN!!! Use it. It won't help with humidity, but it will prevent a nasty sunburn, and a nasty sunburn plus dehydration plus heat and humidity isn't a fun way to celebrate post-race.