Not exactly, but we have a few sayings such as:
"They fight like cat and dog."
"They mix like oil and water."
The above two sayings are good for describing people that do not get on well together.
To describe people that are very different to one another we say:
"They are like chalk and cheese."
However, this last saying does not imply that the two people that are being talked about do not get on - just that they are very different.