MySQL boolean field search vs indexed varchar performance
Short answer for bool vs varchar:  Probably not much diff, but it may depend.
Short answer for bool that is true 90% of the time:  The index is useless.
Long answer...
What percentage of the rows are &quot;is_active&quot;?  If it is more than about 20%, the index won't be used!.
Use reasonable limits on VARCHAR.  Even without that, 'inactive' is only 8 characters, not 255.  So, WHERE status = 'inactive' is not much slower than WHERE is_active.
Is that the entire WHERE clause?  I ask because Optimization requires looking at the entire WHERE clause.  For that matter, then entire SELECT can be important.
Often the query involves
WHERE is_active
  AND other-stuff

In which case, this may be very beneficial, even with 90% being active:
INDEX(is_active, other-column)

But, again, I need to see the details before giving a definitive answer.
And, no, the poor cardinality of is_active is not relevant in a composite index.