What do you think it means to be socially conservative in those communities? I belong to a few of the ones you mentioned, I'm Black, Chinese, Indian and Caribbean and I've lived in Miami my whole life around a lot Cubans, Colombians, Puerto Ricans, Haitians, Dominicans, and have quite a few relatives from those countries in my family through marriage and honestly I don't see Republicans making any long term gains among those communities.
For one the work ethic narrative is nonsensical. I've had a job since I was 15 so have most of the people in my family. Democrats and liberals are as hard working as Republicans. Two, like the white population it's the older generation that tends to lean more conservative and their voting patterns are unlikely to change much. The younger generations of all those communities are less religious and hold fewer socially conservative views. Three, the Republican party itself faces an identity crises. It can't win elections without the rabid racists of the far right. In fact they the Republican majority and they know it and they are going to keep pushing further to right, not moderate to the center.
None of these realities makes it seem Republicans have much chance of long term demographic gains.