Murdoch said that their is Red, Blue and Green and he is a businessman only interested in Green. What can you say about such a... view point. (I was going to say man but I'm not sure he qualifies)
I'm not sure that is true either. Fox is a propaganda arm of the Republican party. Just take a look at Tucker's deal to get exclusive access to all the security cameras on the capital. So while "green" might be a big motivator, "red" is high up the list in Fox's priorities. The two are intertwined at this point but its not like Murdoch has interests in media that isn't right wing.
You state the most important point, that they are intertwined. But what's the reason? Murdoch saw a niche for red swill, where he could make a lot of green, and he went all in. It worked. So now, his business plan is how to most effectively spread red swill. Which will, de facto, make them an arm of the Republican Party.
None of that detracts from the fact that if, in the beginning, Murdoch thought he could make money off of libs he'd be trying to convince people abortion should be legal one year after birth.