The obvious answer to this is "both", but it would be completely missing the point.
I've been thinking about this a lot recently. I don't mean the controversy about these two slogans, particularly. I mean the fact that so much of social and political controversy comes down to rhetoric, and so much of rhetoric comes down to emphasis.
The "black lives matter" crowd insist on "black lives matter", not because they don't believe that all lives matter-- let's ignore the question of the unborn child, for the sake of argument-- but because they think the value of black lives has been neglected, that it needs to be emphasised.
The "all lives matter" crowd respond with their own slogan, not because they don't think black lives matter, but because they feel that there has been quite enough emphasis on identity politics already.
This principle very much applies to controversies within the Catholic Church.
Personally, I'm entirely in favour of social justice, and I think there is such a thing as social justice-- I don't think justice is simply "fair dealing", one person not defrauding or robbing another.
But it often seems as though social justice has become the whole of Catholic teaching, that all bishops and religious orders and Catholic spokespeople ever talk about is racism, immigration, working conditions, housing, etc. etc.
Even accepting that our Faith is based upon Tradition as well as Scripture, the lack of interest that Jesus shows in politics is startling. "Who made me a judge over you to decide such things as that?". "Give unto Caesar that which belongs to Caesar". "My kingdom is not of this world."
Given this, is it so strange that I resent any further pandering to the "social justice crowd", that I'm reluctant to join in their rhetoric in any way? We have more than enough of it!
In the same way, it seems to me perfectly healthy that Catholics resent the lack of emphasis put upon the principle "No salvation outside the Church". The Wikipedia article on this subject shows us how often this has been affirmed, and how stridently, in the history of the Church's teaching Magisterium.
As well all know, it was reframed in a rather less strident form by the Second Vatican Council, but it wasn't abolished. And yet, how would anyone walking into a church today, or reading a Catholic magazine, or looking at a Catholic TV show, possibly realize that the Church is the ark of salvation, and not simply a "faith tradition"?
Is it really so strange that many Catholics are dstraught, today, that rhetoric that has been softened out of all recognition is being softened further, that doctrine that had been so de-emphasized is being de-emphasized even further? We might call the controversies raging in the Church today "emphasis wars", and personally I think they are entirely legitimate.