The mission of the church

Some Christians respond to the social justice movement by framing the issue in terms of the church's mission, or gospel/non-gospel categories. Now, there's certainly an important debate to be had regarding the mission of the church. And it's true that when the church suffers from mission creep, it loses focus, which contributes to doctrinal drift. 

That said, evaluating the social justice movement in terms of the church's mission or gospel/non-gospel categories is too abstract and roundabout. For the more direct issue is that Christian conservatives sharply disagree with secular progressives and progressive Christians on what the social issues should be. We don't see eye-to-eye with what's wrong. Off the top of my head, this is the agenda of the social justice movement:

Affirmative consent

Black Lives Matter

Climate justice (e.g. climate change, sustainability)

Economic justice (e.g. minium wage)

Feminism

Gay rights

Gun ban/confiscation

Immigrant justice

Income redistribution

Intersectionality

Reproductive rights (abortion, "free" contraception) 

Student debt
Toxic masculinity

Transgender rights

Universal basic income

Universal healthcare

White privilege 

Conversely, these are some social issues that concern many evangelicals, libertarians, and/or conservatives: 

Abortion (oppose)

Administrative state (oppose)
Affirmative action (oppose)

Capital punishment

Complementarianism

Due process

Euthanasia (oppose)

Freedom of religion

Freedom of speech

Freedom of association

Illegal immigration (oppose)

Muslim immigration (oppose)
Police state (oppose)

Privacy rights

Property rights

School choice

Self-defense

Parental rights

Surveillance state (oppose)

Tech giant censorship (oppose)

Where the debate comes to a head is over specific issues and political philosophy. "Social justice" is a euphemism as well as an umbrella term. 

The primary reason that conservatives and Christians like me resist the social justice movement is not because I agree with their agenda but think that falls outside the mandate of the church. It's not as though I believe we need to work on those issues, but from a different platform than the church. No, the fundamental objection is that I don't agree with their menu. Indeed, I oppose their agenda. I oppose their priorities. I have a different menu. That's where the argument must be met.