First check for vacuum leaks. The importance of this can not be over emphasized. Even the tiniest vacuum leak will cause problems.
The 2005+ Mustangs are far more sensitive to changes to the intake and exhaust. Need more details on the mods done.
For example, is the K&N intake the type that normally requires a tune? What does the manf say?
Is it an oiled air filter? If yes, this could be the source of the problem. An oiled air filter will contaminate the MAF causing it to read high at idle and low under load. This causes the motor to swing from rich at idle to lean under load.
Clean the MAF. Use only a product designed for the job.
What about the exhaust system? Does the manf state if a re-tune is needed?
2003 GT Convertible (sold & missed)
2000 GT coupe (Craigslist project. Fixed. Now my DD). Windsor to Romeo swap.