Capitalist institutions can 'promote' anything they want as long as they don't use the power of the state to coerce or force individuals to do their bidding [which is is tantamount to serfdom]. This is 'capitalism'.
If a capitalist institution decides to 'get into bed' with the state then it will cease to be a capitalist organization. It will become for all intents and purposes an 'arm' of state. This is 'socialism'.
The terms 'capitalism' and 'socialism' are distinct and mutually exclusive.