I'm not denying that they claim to be republican, but their actions do serve both parties. As such, I don't think their claim to be republican is particularly meaningful.
What's contradictory about a strategist who worked for Ds in 2008 and was working for Rs by 2016? Hell, there's a whole term describing the large set of people who made that shift in that exact time period: https://en.wikipedia.org/wiki/Obama%E2%80%93Trump_voters
This might be a better link: https://en.wikipedia.org/wiki/Party_Unity_My_Ass