When a column contains custom objects as values, these custom objects cannot be compared directly. Data can be sorted and filtered by displayed text. It can be done in the following way:
1) Change the column CellTemplate property that allows an end-user to change object values (e.g., select them from the ComboBox);
2) Set EditSettings for this column and define DisplayTextConverter;
3) Set the SortMode and ColumnFilterMode properties to DisplayText, and set the AllowSorting property to true.
The end-user will always see the data set from CellTemplate, but sorting and filtering will be applied by using text converted by DisplayTextConverter.