Index for column with two possible value
The optimizer evaluates the possible gains of using indexes vs doing a full scan (filtering unwanted rows on the fly). As the ratio of filtered and total rows gets closer to 1 the benefit of using index decreases. The exact tipping point is dependent on the actual data, query, etc. so it's hard to say an exact number when it becomes useless. Generally speaking a 50/50 split is not sufficient for a B+TREE index to work efficiently and most cases full scan will be preferred over using indexes. (Unless it can be used for index-only scans) 

The index is still getting updated regardless of its usefulness in queries.