What does "Don't patronize me" means

The definition of patronize you need is the third one—to treat in a condescending manner, as though you were a not very smart or capable person.

tr.v. pa·tron·ized, pa·tron·iz·ing, pa·tron·iz·es

1. To act as a patron to; support or sponsor: donors who patronize the orchestra.
2. To go to as a customer, especially on a regular basis: We patronize the local diner.
3. To treat in a condescending manner, often in showing interest or kindness that is insincere: felt she was being patronized by her supervisor.

https://www.ahdictionary.com/word/search.html?q=patronize

As the first two definitions show, a sponsor or customer can be called a patron.