Possibly, but churches like Steadfast Baptist that preach death and violence are very rare and usually very small. That Steadfast pastor in Texas who called for execution got more people paying attention to him for saying that then he could have got preaching in church to his tiny congregation, which sometimes doesn't extend into the double digits.
I've written about another Steadfast congregation in the Pacific Northwest whose church is in a strip mall and who have similarly tiny numbers. These churches have next to zero impact on the community, and they have a very hard time growing because of how extreme they are on many issues.
The "gay people should be executed by the government" schtick gets them attention, which is what they want, because not much else has been working for them.
Picketing their miserable little strip mall establishments would likely accomplish the same thing – help them find sympathetic ears attached to people as crazy as they are, but doing little to help LGBTQ people.
The thing is, not even most really conservative Christians go for that kind of ideology. They don't see themselves in the same camp as Steadfast, they aren't calling for violence (even though some of what they are calling for is extremely harmful), and they like to point to wacko extremists to show people how much better they are in comparison. "See, we would never call for people to be lined up against a wall and shot because we are good loving Christians following the teachings of Jesus. But gay people are groomers. Don't say gay in school. No drag queens in libraries."
So what do we get out of picketing nut jobs? We help them spread their message, and we let the people who are causing most of the actual damage feel better about themselves.