Sorry for the clumpsy title (edits would be appreciated).
Hungary has now relaxed the control at internal borders. According to the US embassy in Hungary, Citizens from neighbouring EU countries (Austria, the Czech Republic, Serbia, Slovenia, Slovakia, Croatia, with the exception of Romania) as well as Germany, Switzerland, Lichtenstein, Norway, and Iceland can now enter Hungary without restrictions.
According to the Swiss embassy, citizens of all EU/EFTA states and Serbia can now enter Hungary without restrictions since June 18.
Unfortunately, I have not been able to find an official Hungarian source on these to see if (temporary or permanent) residence permit holders from e.g. Austria (neighbouring) or Switzerland (not neighbouring) can enter Hungary in a similar manner as the nationals of those countries.
For example, this press release says
During today’s Operational Group press conference, Róbert Kiss, Lieutenant Colonel of the Hungarian Police Force, reported that people can now enter Hungary from the Czech Republic, Germany, Austria, Slovakia, Serbia, Slovenia and from Friday Croatia without the need for compulsory home quarantine.
without specifying citizenship/residence/etc.
The border information on the Hungarian police website appears to have not been updated since June 12, it only mentioned exceptions for neighbouring states but not other EU/EFTA countries.