There's no real evidence that nonpartisan blanket primaries (NBPs) discourage extremist candidates. Indeed, two examples suggest that NBPs encourage and reward extremists.
For a long time Louisiana has had NBPs for state and congressional elections. In 1991, David Duke, KKK'er and all-around racist, ran as a Republican in a crowded field of candidates against incumbent GOP governor Buddy Roemer and former Democratic governor and all-around crook Edwin Edwards. Duke and Edwards came out of the first round with the most votes - 32% and 34% respectively. Edwards had the plurality of the votes, even though approximately 64% of the voters wanted a Republican to win. In the second round, a lot of people held their noses and voted for the crook rather than the racist, and Edwards won 61%-39%. If Louisiana had a closed primary instead, it is likely that Duke wouldn't have even run, or, if he had, he would have lost in the GOP primary. Instead, the NBP process encouraged fringe candidates with limited but motivated constituencies, like Duke, to run in the first round, with the hope that they could draw enough votes to survive into the second round.
Likewise, in the French presidential election of 2002, xenophobic racist Jean Marie le Pen managed to go into the second round of balloting with a mere 16.8% of the vote, second only to incumbent president and accused crook Jacques Chirac's 19.8%. Chirac went on to win by a landslide in the second round, as voters of all major political stripes repudiated le Pen, but it's hard to imagine le Pen getting that far in a two-party system like the US.
And that's one of the problems with the NBP. Analysts can look at the results in Washington and California and judge them a success, because it appears that the Republicans and Democrats are getting more moderate candidates.* That, however, is largely the result of the continued predominance of the two established parties, not the NBP. As the French example shows, however, once the two-party system breaks down, that provides an opportunity to extremists of all kinds. Indeed, the Louisiana gubernatorial race of 1991 is another example: there, Duke was, in effect, running as an independent, since the Republican party disowned him. In other words, the NBP works best so long as the two-party system is intact, but the NBP, by opening up the field in the first round to all sorts of fringe candidates, poses a singular threat to that two-party system.
*And that's probably only an appearance. The NBP hasn't prevented the election of such extremists as Rep. Tom McLintock (rated 93% by the
John Birch Society) or Rep. Ed Royce (73%), both members of the House Tea Party caucus.
