Can you activate a fetchland in response to a mill effect to prevent those cards from being milled?

When a spell or ability that mills is put on the stack, players receive priority and may respond before it resolves. Activating a fetchland (e.g., Flooded Strand) is an activated ability that goes on the stack above the mill effect (CR 116.2b, 405.2). The fetchland resolves first, causing you to search for a basic land and shuffle your library, then the mill effect resolves.

Because shuffling randomizes your library, the cards that 'would have been' milled are now in entirely new positions. The mill effect then puts the top N cards of your (now shuffled) library into your graveyard — they simply won't be the same cards (CR 701.13a defines milling as putting cards from the top of a library into the graveyard). You haven't prevented the mill itself, but you've changed which cards get milled.

This is especially useful when protecting a key card you can see is on top of your library, or when an opponent has set up the top of your library (e.g., via Brainstorm) to mill something valuable. By shuffling first, those protected cards get randomized back into the library.

Concrete example: Your opponent casts Glimpse the Unthinkable (mill 10). In response, you activate Flooded Strand, paying 1 life to fetch a Plains, shuffling your library. Glimpse resolves and mills the top 10 cards of your newly shuffled library — the cards that were on top before are likely safe somewhere in the middle.

Note: This only works if the mill effect targets a number of cards from the 'top' of your library at resolution, not if it has already identified specific cards. CR 116.2b governs when you receive priority to activate abilities in response.