Add++, 29 bytes

D,g,@@,T2€BbB^
L,bLd1_Rþ%A$þg

Try it online!

I'm surprised Add++ was this short. Takes input as a list of bits

Add++, 29 bytes

D,g,@@,T2€BbB^
L,bLd1_Rþ%A$þg

Try it online!

I'm surprised Add++ was this short. Takes input as a list of bits

How it works

D,		; Define a helper function
	g,	; called g
	@@,	; that takes 2 arguments e.g. [8 [1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 0]]
	T	; Split into chunks; [[1 1 0 0 0 0 1 0] [0 0 0 1 0 0 1 1] [1 0 1 1 0 0 0 0] [1 1 0 0 1 0 1 1] [1 0 1 0 1 0 1 0]]
	2€Bb	; Convert from binary; [67 200 13 211 85]
	B^	; Reduce by XOR; 0
L,		; Define an unnamed lambda
		; Example argument: [1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 0]
	bL	; Length; 40
	d	; Duplicate; [40 40]
	1_	; Decrement; [40 39]
	R	; Range; [40 [1 2 3 ... 37 38 39]]
	þ%	; Filter false Mod; [1 2 4 5 8 10 20]
	A$	; Push the argument below; [[1 1 0 ... 0 1 0] [1 2 4 5 8 10 20]]
	þg	; Filter false on g; [1 2 4 8]