Weak polyampholytes and globular proteins among them can be efficiently absorbed from solutions by polyelectrolyte brushes or microgels even if the net charge of the polyampholyte is of the same sign as that of the brush/microgel. We use a mean-field approach for calculating the free energy of insertion of a probe polyampholyte molecule into a polyelectrolyte brush/microgel. We anticipate that the insertion of the polyampholyte into similarly charged brush/microgel may be thermodynamically favorable due to the gain in the cumulative re-ionization free energy of the pH-sensitive acidic and basic residues. Importantly, we demonstrate that the polyampholyte (protein) charge sign inversion upon transfer from the bulk of the solution to the brush/microgel does not provide sufficient conditions to assure negative re-ionization free energy balance. Thus (in the absence of other driving or stopping mechanisms), charge sign inversion does not necessarily provoke spontaneous absorption of the polyampholyte into the brush/microgel.