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When doing salting out it's been said that the salt being used should be neutral, meaning both acid and base which make the salt should be categorized as strong acids or bases. Why is that?

For example, $\ce{NaCl}$ could be used as a salting out salt in principle, because $\ce{NaOH}$ is a strong base and $\ce{HCl}$ is a strong acid but using $\ce{NaCH3COO}$ is not right because $\ce{CH3COOH}$ is not a strong acid.

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    $\begingroup$ If you add the salt of a weak acid or weak base, what new equilibrium will result? How could this new equilibrium affect the proteins present in the solution? $\endgroup$ – J. Ari May 5 '17 at 15:19
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    $\begingroup$ Please don't use irrelevant tags. $\endgroup$ – M.A.R. ಠ_ಠ May 7 '17 at 16:32
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"Its [sic] been said" is inadequate contextualization. Many organic solutes are potentially capable of being ionized, especially in aqueous solution. Maintaining aqueous media at a neutral pH will for most solutes minimize this (undesired) effect. For instance, in the following reference (note date and distinguish between what is observational (and thus probably "true") and theoretical (based on what is likely to be incorrect chemistry)), read the last sentence on page 531 over to 532. http://www.jbc.org/content/33/3/531.full.pdf

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