In particular, we demonstrated that for the uncharged chain ion-specific effects only are at work and the collapse is mediated through repulsion and swelling by attraction regimes; the salting-out power of ions follows a direct Hofmeister series characterized by a linear regime up to intermediate salt concentrations. For the charged, cationic polymers we demonstrated ionspecific screening and bridging at low salt concentration and strong ion-specific direct interaction effects at high salt concentration. We made an important theory-grounded observation of an isospheric point, i.e., salt concentration at which ion-specific effects vanish and the Hofmeister series inverts. That is, the salting-out power of ions follows a reverse series bellow the isospheric point and a direct one above. The isospheric salt concentration depends on the polymer charge fraction. Our observation is supported by experimental data for ELPs, as well as for other positively charged proteins. For the anionic polymers our mean-field theory predicts a non-linear and for weakly hydrated (very attractive) anions also non-monotonic change of the LCST with salt concentration. At low salt concentrations, the strongly hydrated cation determines the screening and osmotic pressure in the polymer phase, only mildly modulated by the anion type. In the limit of high salt concentration, the ion-specific direct interactions drive the polymer collapse, or swelling, respectively, which results in two regimes of salt action. Consequently the direct Hofmeister series is followed in the whole concentration range, unlike for the cationic polymer.