It would depend on the dye. The picture you gave doesn´t look like it is dyed water. If I were to consider a colour change in my pool, I would first have to identify what the colour of it currently is naturally. This is a reflection of colours surrounding the water and what colour the pool is painted. Most are painted a light aqua colour, so you won´t get a pink colour or anything that is absent of that colour wavelength. You could go with a darker green-blue (but that would look gross) or you could go a darker blue.
If the pool surround is white and painted white, you´d be able to play with more colour choices.
You could use colours that are skin safe, like those used to colour cosmetics. DON´T confuse edible colours with skin safe colours as they are not the same. Also, you don´t want to turn your bathers skin funny colours, so you need to use only a very limited concentration. and lastly, you have to consider the pH of the environment you are putting the colour into and if the colours you are using are pH sensitive.