Can (or should) data dominated by two values be treated as categorical? Problem. I have few data sets containing real values (aka observation and prediction). >85% of data values are oscillating between two values exactly (e.g. 0 or 10), while the rest are real numbers in between (thus, it is dominated by only 2 states). I am planning to choose a method to calculate similarity (e.g. pair t-test or McNemar's test).
Question: Could or should this data be treated as numerical? Or, is more appropriate to treat it as categorical?

The short answer is that there's nothing wrong with doing this per se, and it can be useful when your raw data isn't appropriate for something like a t-test. Coding the data as above or below $5$ is probably the most sensible approach in your example.
However, doing this slightly changes the nature of the questions you're asking of your data, and throws away some information that might be worth trying to capture with a more sophisticated model fit to continuous data, so ultimately you have to exercise judgement.
