I'm not sure whether the rules differ in Hungary, but it's probably the same as in Germany and Switzerland:
If you're sweaty, always shower before entering the plunge pool. (You don't have to observe this if the "plunge pool" is a natural body of water such as a lake.)
If the plunge pool is in the sauna area, then you should wear the same attire ...
Per TIMATIC, the database used by airlines:
Passengers are not allowed to enter.
This does not apply to nationals of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czechia, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Ireland (Rep.), Italy, Latvia,
Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, ...
What are travel restrictions when I will go to Lisbon, Portugal? Should I go to quarantine?
Right now, in Portugal there are no quarantine-on-arrival measures in place.
On the UK GOV page for Portugal, it says:
Air - Mainland Portugal
You will be subject to health screening on arrival. Your temperature will be checked and if it is high or you show signs of ...
As a US citizen, you generally do not need a visa to enter the Schengen area for short-term tourism, family, study and business purposes.
Travel medical insurance is not mandatory for visa-free third country nationals. Although, it is strongly recommended that you get a travel insurance. These insurances are usually cheap for healthy adults (except seniors) ...