For me, race is distinctly physical, whereas ethnicity is cultural. The debate around whether the concept of race should even exist due to how problematic it is to try and define distinct racial groups is an interesting one, but for a workable definition, I'm going to use it to mean distinct physically different groups of humans.
In terms of your other definitions, its distinct from them because:
Tribalism - is just problems based on tribes, but tribes can be defined by many characteristics, this could or could not include race/religion ethnicity etc.
Ethnicity - this for me, can contain small physical differences, but is mostly cultural in nature.
Ideology and religion are obviously different,
But the key thing for me, is that all group conflict can be a mixture of some or many of these factors. For example, staying local to where I am at the moment, conflict between the Manchu + Han people in China is an ethnic conflict, not a racial one.. but persecution of Persians immigrants by the mongols, was racial and ethnic. Conflict between th Han and the Uyghur, is both ethnic and religiously motivated. etc. You can go back through history and find examples of combinations of all types of prejudice, including racial prejudice.
The fact that we defined it, and tried to justify it with science, and created the modern concept of racism doesn't mean that what existed before it was defined wasn't racism. It just means it wasn't understood as such. A child who doesn't know the concept for an action they take, is still taking the action, even if they aren't able to explain it using the same language or ideology of an adult etc. (another example would be, was a man, in ancient times, sleeping with a girl who was 11 years old, rape? Back then it wasn't, and the modern definition/concepts surrounding rape didn't exist for a very long time etc. but I would still say it was rape.)
For example, a quick google brings up this;
https://www.independent.co.uk/news/science/archaeology/saharan-remains-may-be-evidence-of-first-race-war-13000-years-ago-9603632.htmlWould either side in the war have defined it as racist, or even been aware of the concept of race? No.. but to the best of the researchers knowledge, they were killing another group based on their race. Its thought they wouldn't have been able to communicate with each other, so the idea of it being based on ideology seems less likely then it being based on racial (physical) differences, and the desperation of competing for resources. If they are correct, then its a very ancient example of racism, by our modern definition, far far before any modern western civilization.