I've never seen security between US arrivial and non-schengen departure gates. Where would this security checkpoint be?
I thought if you transfer from Non-EU to EU you always have to go through security? No idea how this is implemented in MUC.
Edit: BUD flights leave from G39-G48 or G81-G84, which is non-Schengen on the G level. Your flight from ORD arrives on level H, so you will need to go down one floor. Just follow the signs to your gate.
Here is a detailed terminal map:
http://www.munich-airport.de/Mediapo...enenplanT2.pdf