Its a personal preference, but I understand Animal Kingdom gets mentioned for not rain friendly. I first went Animal Kingdom in 2001 and the other 3 parks in 1991. Animal Kingdom in some parts is spread out.
The park is not as sheltered as some other WDW parks although there are people that like see animals during the rain.
That park though is a bit of a wait and see after Tropical Americas since Chester & Hester area was all outdoors in terms of rain.
I went to WDW for years in late August through a couple days after Labor Day. That time of year is a must for a person to bring ponchos.
I agree it's not quite the same density but it is leagues better in the rain compared to Epic and its not even close.
The only rides that close in AK due to rain is Kali & Everest as of now (which I have seen both running in rain with no serious winds/lightning)
Safari, Wildlife Express, Dinosaur (soon to become Indiana which won't change), Nemo, Lion King, FOP, River Journey
not even including ITTBAB/Encanto/Carousel which will also all not close for regular rain (but the carousel prob will for strong winds + rain)
This means that 77% of the park is still open even with some pretty bad weather in the area, if its just rain, 100% of the park is usually open.
With the new expansions/replacements, 83% of the park's attractions will be open during the inclement weather and still 100% during the regular rains. For Disney's "worst park for weather", that is some GREAT percentages. For comparison, noting how Werewolf, Stardust, DK, Yoshi's, Rally Racers, Wing Gliders, Fyre Drill all go down in the rain... this leaves only 46% of all attractions are open during inclement weather, around half of Disney's worst park for inclement weather.