But crosstab takes text strings as parameters. How then do you use \set variables in crosstab queries?
You need to dynamically write the textual query you want to send to the crosstab function. In particular that means writing it using "format()" and then substituting the values into the query via placeholders.
Roughly like:
SELECT * FROM crosstab(format('SELECT * FROM %I WHERE %I = %L, :'tbl_name', :'col_name', :'compare_value'));