And you're right, the non-profit-status doesn't imply that, they could just as well do the same as a commercial enterprise. It would be more obvious that way.
Would Mozilla make the step to ship an adblocker with Firefox? It would certainly be what their users want (the most popular extension by far being uBlock Origin), but it would pretty much decrease their worth to Google to zero, hence kill the funding. And there's your conflict of interest.