We should seek common ground while maintaining different opinions. Does this sentence make sense?

Grammatically it is fine, but the message is somewhat awkward, because it sounds a bit as if you are saying that there can be common ground even in those areas where the opinions are all different—and it is not clear how that would work.

You probably meant to say something like

…while respecting each other's differences.

Or perhaps this:

We should seek common ground where possible while respecting our differences where it is not.