First Equal Protection clause from the 14th Amendment applies to only states and not federally. [1]
Second, It is extremely hard to prove that discrimination happens while all other things are equal . Rarely all other things are also equal as there are many strongly correlated factors with race[2] that can adversely impact conviction, for example being black on average would be poorer and would more have a court appointed attorney who is looking to close a case(given his load) rather than win for each defendant and push a defendant to plea out than go to trial etc. Is this directly because he is black ?
Race, age and gender are objectively measurable [3], "attractiveness" is lot more subjective to eyes of the beholder. How do you even come up with a scale for legal purpose of measuring bias like this ?
U.S. follows trial by jury, by definition that means the jury of peers are to take the law and your entire specific example and act with full freedom as they see fit ( even nullify laws if they wish to do so). In a such a system there will be biases, because people are inherently biased. While there are some efforts to reduce this, like no all white juries against black defendants etc, unless there is fundamentally different system biases can not be eliminated.
The biggest determining factor is Money. Richer you are, less likely to have trouble with law, and get away with a lot. White, young, female and attractive correlates to being rich. Sadly that is how the world works.
[1] There are similar protections in the 5th Amendment Due Process Clauses that can be applied at a federal level.
[2] Similar examples to other factors as well
[3] Race and Gender can have some ambiguity but in most cases it is clear