What percentage of African-American Republicans are conservative?

The 2018 Cooperative Congressional Election Study is a large-scale survey project which contains a dataset formed of a nationally representative sample of 60,000 American adults.

Restricting responses to those identifying as 'Black' when asked 'What racial or ethnic group best describes you?', and further restricting these respondents to those who answered Lean Republican, Not very strong Republican, or Strong Republican when asked for their party identification, we are left with 408 respondents.

The dataset includes two questions which can be used to answer your question. Firstly, the 'ideo5' question, which asks "In general, how would you describe your own political viewpoint?", and gives a five-point scale from 'Very liberal', to 'Very conservative', and secondly, the 'CC18_334A' question, which asks 'How would you rate each of the following individuals and groups?: Yourself', and gives a seven-point scale.

The responses to both questions are shown in the bar charts below. Restricting the responses to both questions further to a three-point scale, Liberal, Moderate, and Conservative and excluding 'Not Sure', we get 38:95:249, and 45:58:296 respectively. This relates to approximately 10% liberal, 25% moderate, 65% conservative in response to 'ideo5', and 11% liberal, 15% moderate, 74% conservative in response to the finer-grained 'CC18_334A'.