Any and its extensions anything, anywhere, anyone, etc. is a negative polarity item. In other words it is more usual in negations than its some (something etc.) equivalent. For example:
- I don't have any money. (?I don't have some money.)
- I don't have anything to wear. (?I don't have something to wear.)
- I don't know anyone who thinks that. (?I don't know someone who thinks that.)
The sentence They disregard social conventions without being conscious that they are doing anything extraordinary is a far less clear-cut example of negation. But negative polarity is present in the word without. The sentence could be rephrased:
They disregard social conventions and are not conscious that they are
doing anything extraordinary.
This explains the use of anything in the original sentence. Nevertheless, something is also fine in this context - albeit with, for me, a different connotation.
In the original version, the writer is simply saying that eccentrics don't think they are doing anything extraordinary. I get no sense of whether the writer thinks they are or are not doing anything extraordinary.
The version with something (They disregard social conventions without being conscious that they are doing something extraordinary) can be interpreted that the writer does believe they they are doing the extraordinary.
Such an interpretation is given some support by the sentence that follows:
This invariably wins them the love and respect of others, for they add
colour to the dull routine of everyday life.