I went to the LCWR website and found it to be inspired more by radical leftist ideology than by Christianity. A good example is a statement on racism which runs like this:
Racism in its institutional form continues because some people assume, consciously or unconsciously, that white people are superior. Therefore, the dominant race of whites develop and maintain institutions that privilege people like themselves and give less credibility to the contributions of other peoples and cultures. White privilege often goes unnoticed because it has been internalized and integrated as part of one’s outlook on the world by custom, habit and tradition.
Peggy McIntosh, author of White Privilege: Unpacking the Invisible Knapsack, wrote about her experiences of white privilege. Her education gave her no training in seeing herself as an oppressor and advantaged person. Any work to benefit others was to allow "them" to be more like whites. She described white privilege as similar to an invisible weightless knapsack of special provisions, assurances, tools, maps, guides, codebooks, passports, visas, clothes, compass, emergency gear, and blank checks.
Social rules about what work is, who works for whom, how work is compensated, and the social process by which the result of work is appropriated operate to establish relations of power and inequality. These relations are reinforced by a systematic process in which the energies of the have-nots are continuously expended to maintain and augment the power, status, and wealth of the haves. This structural relationship between social groups is exploitation. (Iris Marion Young, Justice and the Politics of Difference)
That's a left liberal analysis of race, not a Christian one. The left liberal analysis goes like this:
i) The aim of politics is to disband unchosen social ties so that we are left as self-determining individuals subject to the same autonomous conditions of life
ii) Our race, just like our sex, is predetermined rather than self-determined and therefore must be made not to matter
iii) But race does still seem to matter. Some races do worse than others in education, in employment, in crime statistics etc.
iv) This is to be explained by a dominant group setting themselves up as a false racial category (whites) in order to enjoy an unearned privilege at the expense of an oppressed group (blacks)
v) Whiteness is therefore an artificial and oppressive social construct which only those whites seeking supremacy would want to uphold.
vi) White privilege is also to be regarded as systemic, as the institutions and culture of society were created to serve it
vi) Whites should therefore seek to deconstruct themselves and their society as whiteness is a uniquely immoral category associated with race supremacy and privilege
When the nuns endorse Peggy McIntosh's complaint that she was not educated to see herself as a white oppressor they are following not Christianity but left-liberalism.
Christianity cannot follow along the same lines as left-liberalism as Christianity accepts that we have a creator which means that we do not autonomously self-create who we are. To put this another way, if you believe that you are autonomously self-created, then you do not have the Christian view of man's relationship to God.
So Christians will focus on different things to liberals. Less on achieving equally autonomous life conditions and less on making predetermined qualities not matter.
If race does matter in certain respects that does not invalidate the core purposes of Christianity. It does not require Christians to resort to a class/oppressor analysis or to seek to deconstruct white people and white society.
The minds of the nuns of the LCWR have been colonised by a secular ideology. They may as well be just any other kind of leftist academic or political activist. They have made themselves redundant as nuns and therefore it is no surprise that their numbers are falling so rapidly.