True, though I would not take Trump as a good example of a conservative. He certainly plays hard on some of the conservatives' currently favorite instruments and sings some of their favorite songs, but that doesn't mean he is ideologically one - just that he wants their votes, and they are willing to ignore (not all of them, mind you - there's a sizeable anti-Trump sentiment among the conservatives) his mismatches with their agenda because they perceive the matches are more important.
I don't know how you can look at media organizations like the New York Times and not see that they clearly have a comically overt agenda in how they talk about him and represent his positions.
NYT certainly has a known political bias, and that's no secret to anyone paying attention. Trump highlighting this bias and addressing it would not be a problem. Trump hinting at using state coercion to influence the content of NYT reporting is a huge problem and runs directly contrary to the 1st amendment (not that his presumptive opponent doesn't have her own huge flaws in that department) and US free speech culture.