Might be a too extreme solution to the specific problem that the score would be too broad if we allow such power, nevertheless, everyone would understand such a step, but please consider that the score might be too broad, too, since you have many specific problems to tackle not everyone is even knowing of. This means failing much in one category, but, I'm exaggerating right now, winning in another.
If the target of Clash of Code is to improve on a major scale, then ignoring any score if you turn off some category would be the way to go. (this way, being able to toggle categories wouldn't make sense either, since it misses the target of CoC, but it would be still fun to be able tho)
But if the target is to improve specific skills, then a more specific score might be the way to go, meaning a specific rating for every different category for which you have the power to turn on or off. However, this will lead to the problem of how to organize this, since you already get a category for every single language, because of code golf. (Java vs Ruby, who'll win?)
Having such an amount of possible scorings seems to make it overly complicated, doesn't it?
I would suggest, because I really like the idea of improving in many ways, to use just one overall score, but to calculate that in a different manner, e.g. count less points the more you do specific challenges of the same configuration. It makes no sense to count even more less points if you switch it sometime, since it would be completely different. But even this way, every score should be displayed somehow. Sadly I have no suggestion for this, I suck at design and I think there is... What about a pie-chart? The more same (meaning not so broad) challenges you do, the less percents for the chart you get. The overall CoC score is the sum of every category displayed in that chart multiplied by it's percentage. Something like that maybe. … Anyways,
Depending on what Clash of Code wants to archive the solution is different, either use one very broad score or a more specific one. If the more specific one will be the way to go, then there will be much more stuff to think of.