What I understand from your question is that you are doing some kind of dye adsorption (loading) experiment in which you see an effect of pH. If the mechanism of adsorption of the dye is electrostatic (e.g. cationic dye on an anionic substrate) and the binding sites on the substrate are mildly acidic or mildly basic, than yes the extend of dye-binding will depend upon the protonation degree of the binding sites and thus on solution pH.
What also influences your adsorption, in case the mechanism is electrostatic, is the salt concentration in your test solutions. In case the salt concentration is high, there are many ions that compete with the dye for a binding site on the substrate. Hence, if you want a good model study, use solutions that are buffered for pH and ionic strength.
For a practical study, alas, you have to measure the pH and for instance conductance to know the approximate salt concentration, and run your tests under those conditions, making sure not to dilute or add acid/base to your test-solutions.
I am really thankful to you for sharing informative ans. reg my question, but my question is, we have already optimized the initial pH with a constant dye loading, and we have observed that the pH of the solution changes according to dye loading. Hence, how to interpret the this kind of relation...
Did you buffer the initial pH? If it is not buffered it can still change if the ions in solution are not able to maintain a stable pH. In that case it might be that loading the dye results in the displacement and release of acidic or basic species from your substrate. If the initial pH is buffered by a low concentration buffer, lets say 1 mM, it should remain stable (within certain limits).
Is perhaps the dye acidic or basic or does it contain acidic or basic impurities? Most dyes have some acid-base properties and for them to bind they may have to (de)protonate, which may cause your pH change. Can you measure the pH of the dye solution to see if it is different from your solvent?
Else, I also have no explanation for this observation.