The First Amendment ends where private property rights begin
Being a "journalist" does not mean you get to invade private property and disrupt what people are doing there.
There is a classical (small L) libertarian saying that "I can swing my fist as much as I want until it touches your nose." Putting aside the problems with this oversimplified argument, the message is clear: Your rights end where someone else's rights begin. You do not get to do whatever you want if it involves harming others, and harm can take many forms.
To put it simply: You do not have the "right" to enter private property and confront the pastor of a church while the service is happening. There are limits to the First Amendment. It is not a license to do whatever you want to do, whenever you want to do it. This is one of them. Your right to petition government for redress of grievances does not give you the right to scream into a bullhorn outside of an elected official's bedroom window at 3:00 am either.
Former CNN anchor Don Lemon "covered" the protest, and was defensive, defiant and petulant when criticized for his behavior. But being a "journalist" does not mean you get to invade private property and disrupt what people are doing there. It does not give you the right to "cover" a "protest" where the "protesters" are also invading private property and harassing churchgoers. Your so-called "freedom of the press" does not allow you to violate private property rights.
What, exactly, is the point of storming into a church and harassing the people worshiping? Do you think you are going to change even one single mind, or are you going to push them farther away from your position? If there were people in the congregation who could be convinced by a reasonable argument, you have closed the door to that. You probably succeeded in broadening your phylacteries to prove your righteousness to each other and to fellow Leftists who are cheering you at home. Yay for you.
The point of a protest is not to disrupt or make people uncomfortable. The point of a protest is not to parade your virtue. The point of a protest is to change public policy, raise awareness, and change individual minds. Acting like a jerk and berating people in church will do none of those things. It will only turn people against you. But hey, it makes you feel better about yourself, right?