The short answer is both yes and no - it simply depends on what material the bathtub and chimney are made from. Apparently identical materials can differ in how well they withstand salt water - there is stainless steel that tolerates salt water and stainless steel that does not.
The advantages of choosing a bathtub that tolerates salt water are many - if you have access to lake or seawater near your cottage or home you can use it just as well as fresh water. It is also an advantage in places that risk being affected by water rationing due to low water levels.
Our outdoor bathtubs tolerate salt water. The shape of the bathtub also affects water consumption - a bathtub can require anywhere from about 800-2000 litres of water depending on size, whilst our smaller tub Sotiga Grytan requires only 470 litres and our larger bathtub Bohemen requires 600 litres. This means they heat up faster, require less wood and weigh less.