Thank you! I have never been there, but from what I've read, it sound like the rule recently became more strict.
https://szechenyibath.com/can-children-go-to-szechenyi-baths-szechenyi-bath-faq/
"Kindly note that only older teens, over 14 years old, are allowed to enter the hot water thermal pools in Szechenyi Bath. Underage (0-14 year old kids) are, unfortunately, not allowed, not even with a parent. If the pool master notices such an incident, guests will be asked to leave the pools....Kindly note that there is a third outdoor pool of 38 degrees that cannot be used by kids, as the mere temperature of the pools means a potential increase in the stress for the cardiovascular system of kids, whose body is not fully developed yet to be able to cope with the heat of the bath waters."