You are right to be concerned. There are many similar movements in other dioceses that have involve the diocese or parishes in partnerships with groups that exploit the Church’s credibility, and often disagree with Catholic teaching. The experience in my diocese, and others I read about, is that there is no spreading of Catholic belief, but only co opting the Church for secular causes.
There is not much you can do, other than monitor it. They can always try to justify any alliances or shared projects, and you will get labelled a right wing conservative.
What you can do is check out something specific: if any leaders or organizations have taken a position on abortion opposed to the Catholic position, gather documentation. The diocese can ignore you if you complain about “leftists”. But if a given speaker, for instance at a Catholic school has taken a pro abortion position, forward documentation of that to the diocesan prolife office. Ask them to intervene. Send a copy to the parents guild, and to alumni association. Catholic institutions can ignore you, especially if you are vaguely talking about “leftists”. They can’t ignore their funders.
If an organization has taken a pro abortion position, and the diocese is proposing to partner a Catholic organization with that organization, do the same thing. If the local Catholic organization gets funded by the CCHD, contact the CCHD. They are supposed to have guidelines against this. If the diocese gets money for social programs from some other source, such as K of C, and if they plan to involve a proabortion organization, contact the K of C.
I realize abortion is not your particular concern yet, and should not be the only red flag for Catholics. But at the moment, it is the one red flag that might wake up some Catholics. And, tragically, the great majority of peace and justice advocate organizations have taken a trackable position for abortion. It might be the only handle you can grab onto.
It will take a little work on your part, find out which coalitions those other groups are part of, and find out who is funding the diocesan programs that would be partnering. Whatever you do, be brief, and focused, don’t bring up issues in general. You want the focus to be on the one thing that can limit them.