Not really. Within the Court, the divide is primarily between originalists and pragmatists. This has been a fight going back a long time in legal theory. It had been dominated by pragmatists since the 1920s and the tide started to turn in the late 1980s. The current Court is dominated by originalists.

It has little to do with political parties even though originalist thought is more aligned with conservative social and political thinking and pragmatists are more aligned with progressive thinking.