Some proteins can act as thickening agents and increase the viscosity of the solution, while others may have little effect on the viscosity. However, it is important to note that the concentration added matters, and higher levels of proteins will definitely affect the viscosity of the solution.
To maintain the approximate density of the combined solution, it is important to choose a protein that is soluble in water and does not form large aggregates or networks that can significantly increase the viscosity. Examples of such proteins include whey protein isolate, soy protein isolate, and pea protein isolate.
Adding a small amount of protein to water, such as 1-2% by weight, is less likely to significantly thicken the water compared to adding a higher concentration of protein.