I am aware this was reported here: codepress/admin-columns-issues#1187
However it seems to me that one of the original discussions (https://www.admincolumns.com/forums/topic/getting-403-forbidden-when-searching-posts/) of this issue incorrectly identifies the issue as being caused by the json string in the url, when in fact it is being caused by the use of SQL terms in the query.
Seems to me there is room for Admin Columns Pro to not use SQL terms (AND or OR etc.) in the smart filter