K (ngn/k), 99 13 bytes
Solution:
~=':,/+2\(7#2)\'
Explanation:
~=':,/+2\(7#2)\' / the solution
2\ \' / convert toeach
base 2 ( ) / do this together
+ 7#2 / transpose2 2 2 2 2 2 2
,/ / flatten
=': / equal to each-previous?
~ / not
Notes:
- +4 bytes to support strings consisting only of 6-bit chars