There is an underlying abstraction beneath a very technical dispute about commingling contaminated materials. An uncontaminated domain is fit for holy practices, but not if it contains materials that are forbidden for use in holy practices. Even so, it has not yet been determined (at least through the present daf) that the elimination of that which is contaminated may be effected simultaneously with the elimination of that which is forbidden. The resolution depends on whether it is permissible to contaminate a forbidden object in the process of destroying it.
Daf 338 (Pesachim 15a-15b)
R’Chanina “testified” that the Kohanin burned both meat contaminated rabbinically and meat contaminated biblically in the same fire, suggesting this is justification for burning contaminated and uncontaminated chametz together on erev Pesach. (And also suggesting that the priests were guided in this matter by the rabbis? Is this an anachronism?) But the rabbis see a distinction between commingling products with different degrees of contamination and commingling uncontaminated and contaminated products; in the latter case, the commingling initiates contamination of that which was not contaminated rather than simply advancing it in products previously contaminated.
Can one contaminate a material “with one’s own hands” to prevent monetary loss of materials that would otherwise be exposed? (Answer: Only if the loss will be “substantial.”)