In any case. WSJ isn't more objective that NYT. It's just further to the right, which is why it appears objective to someone on the right.
No, they were not. Maybe replacing 'white' with other races will help you to gain some perspective: https://pbs.twimg.com/media/DjnUykIUUAAifwH.jpg:large
(That is, putting the tweets into a different context doesn't demonstrate anything about what was meant when they were twote.)
In any case. WSJ isn't more objective that NYT. It's just further to the right, which is why it appears objective to someone on the right.