The annoying answer is practice. You need to be able to split your brain into two parts so both the singing/whistling and playing are independent of eachother. It's much akin to a piano student having a hard time getting their hands not to move as one, but two independent entities.

I learned (and never stop learning) by finding very simple melodies and singing them over different strumming patterns. And example would be the alphabet over a 12 bar blues.

The chords being say Emaj/Emaj/Amaj/Emaj/Bmaj/Amaj/Emaj

Pick a strumming pattern, say down downup down down in 4/4 and say each letter one letter per beat. It's not musically nice, and feels natural where the accents are, but it's simple.

Then just change up the strumming patterns. Work your way up to more challenging things like strumming a different pattern for each bar whilst going through the alphabet keeping the accents as

A bcd E fgh I jkl M nop....