I understand where you are coming from, and you are right in some aspects. But there's more context to why there is a narrative that minorities generally "seem" to lean on the American left. It doesn't really have anything to do with how life is represented in the media - after all, minorities don't really consume American media even in this country.
Minorities are by and large generally more culturally conservative than the majority of the West. The only difference is the approach to communalism versus individualism, but the American conservative affinity towards individualism is largely a classical liberal idea. Minority communities are not blind to that, several aspects of progressive politics are incompatible and the media hasn't changed their mind. For instance, the gay and black community is very splintered, and progressives have been able to manage that. Left-wing literature and academia acknowledge this as well. Add influences of the Vietnam War, and you will get a vastly conservative community.
However, party politics in America do not subscribe to a consistent frame of ideologies. As cultures began compounding over the past 60 years, identity is the mainstream approach for appealing to bases. The parties have chosen a side.
A majority of minority voters have weighed the cost-benefits of choosing between their conservative principles or a stronger representation of their people, and found one side more accommodating. Quite literally, the biggest downfall to the advancement of conservative ideals in America is probably one specific party's refusal to appeal towards minority communities. It was true before Trump, Trump only exposed this reality of the Republican base. There could have been a conservative revolution.
One final point. Asians has had to deal with issues of systemic and structural discrimination from both sides of the aisle. The issues go far broader than higher standards of university admission. Very little to do with their affinity towards specific ideologies.