UPS does hire felons but only on a case by case basis.
UPS the company does not have a blanket policy against hiring of felons.
Although a felon that has more recent convictions, especially any convictions related to violence or theft may have more challenges in getting hired but you can still apply for a job with UPS.
Having a clean driving record is required for driving jobs with UPS although working in the UPS sorting facilities don't require any drivers license or clean driving record.
If your felony has been longer than 10 years and you otherwise have a clean record with no more criminal convictions or trouble with the law in that time then you're more likely to get hired.
I've worked with a few people in UPS that were convicted of felonies and served time in prison and they were hired and turned out to be good workers.
As part of their standard hiring process, UPS does conduct thorough background checks, which include performing criminal record searches.
These checks when deciding to hire someone help the UPS make informed decisions about an applicant's suitability for various roles.
Non violent crimes and misdemeanors that are unrelated to the job may also not significantly affect decision making in whether to hire you or not at UPS.
However, even non-violent felonies such as grand theft could be a disqualifier for a job involving handling packages in transit with UPS.