Yes, you can apply for a work permit. The Immigration Office is open, and they are processing applications as per usual.
Most consulates are open – but not all of them, you will have to check with the consulate closest to your place of residency, and you will most probably need an appointment.
If you are applying in Hungary, you will definitely need to book an appointment with the immigration office. At the same time, you can still use the “Enter Hungary” portal to manage your affairs and submit your application.