Measuring categorical (race) and two continuous varibles

I need your help to identify which test I have to implement for measuring the correlation of one categorical and two continuous variables. In my study I have two constructs:
1- information consumption from credible sources (CS)--4 items(ie., information consumption from CDC website)​
2- information consumption from incredible sources(NS)--3 items (i.e., information consumption from celebrities' social media account).​
Both used a 5-level Likert scale.

My question is, how can I figure out which race used more credible sources and which one used noncredible sources?
For instance, I want to know do White people used credible sources more than noncredible sources? what about Asians and African Americans?

--My own thoughts>>
I have developed a continuous measure for each CS and NS( mean of the consumption for each individual) and put them as two factors in the repeated measure ANOVA analysis. But I'm not sure if I can do this or not, because these two are not mutually exclusive. Also, I refused to use cross-tabulation because I think the condition for that is to have your dependant variables to be mutually exclusive.

I would appreciate if you can confirm I can do repeated measure or suggest a test to investigate my question.