I am trying to optimize this query that sorts posts by reputation field (1st) and then id field (2nd). Without 1st field query takes ~0.25         
        
Inflate-deflate -- LEFT JOIN inflates the number of rows, GROUP BY then deflates.  The inflated number of rows is costly.  Instead, focus on getting the ids for the desired rows before doing any JOINing.  With luck, you can get rid of the GROUP BY.
WP schema -- This is an EAV schema which sucks when it comes to performance and scaling.
What indexes do you have? See this for how to improve the meta table.
Complex ORDER BY.  This leads to gathering all the rows (after filtering) before sorting and doing the LIMIT.  Rethink the ORDER BY clause, if possible.
After you have done what you can with my suggestions, start another Question to continue the refinement.  Be sure to include EXPLAIN SELECT ... and SHOW CREATE TABLE.