E. coli single-stranded-DNA binding protein (EcSSB) displays nearest-neighbor (NN) and non-nearest-neighbor (NNN)) cooperativity in binding ssDNA during genome maintenance. NNN cooperativity requires the intrinsically-disordered linkers (IDL) of the C-terminal tails. Potassium glutamate (KGlu), the primary E. coli salt, promotes NNN-cooperativity, while KCl inhibits it. We find that KGlu promotes compaction of a single polymeric SSB-coated ssDNA beyond what occurs in KCl, indicating a link of compaction to NNN-cooperativity. EcSSB also undergoes liquid-liquid phase separation (LLPS), inhibited by ssDNA binding. We find that LLPS, like NNN-cooperativity, is promoted by increasing [KGlu] in the physiological range, while increasing [KCl] and/or deletion of the IDL eliminate LLPS, indicating similar interactions in both processes. From quantitative determinations of interactions of KGlu and KCl with protein model compounds, we deduce that the opposing effects of KGlu and KCl on SSB LLPS and cooperativity arise from their opposite interactions with amide groups. KGlu interacts unfavorably with the backbone (especially Gly) and side chain amide groups of the IDL, promoting amide-amide interactions in LLPS and NNN-cooperativity. By contrast, KCl interacts favorably with these amide groups and therefore inhibits LLPS and NNN-cooperativity. These results highlight the importance of salt interactions in regulating the propensity of proteins to undergo LLPS.