A couple of years ago, our company rebranded. We now have two sites. The old domain (our old brand) consists of content related to our current brand, but this old site also has a large unhealthy backlink history. This history received a flag in Google's webmaster tools for those unnatural links.
If I 301 redirect all related content from the old domain (old brand) to our current domain (current brand), will the new backlink profile be associated with those unnatural backlinks and hurt my current domain's backlink profile and organic traffic?
For branding, it is important that we do this, but for lead generation, the old domain is performing in traffic equivalent to our current domain.