There can be no presumption of heresy due to mere belonging to the Conciliar Church precisely because the Conciliar Church masquerades as the Catholic Church.  Every Catholic on any side of the Great Western Schism intended to adhere to the Catholic Church and professed adherence and submission to the Catholic Church.  There are many in the NO who profess that it is required to submit to the Magisterium as their rule of faith, and that's the essence of having the formal rule of faith, even if they happen to be materially incorrect on what that Magisterium teaches.  So there can be no presumption or assumption that someone who belongs to the Conciliar Church is a non-Catholic or a heretic.  In fact, unless one has contrary information about any given individual, charity requires that we give them the benefit of the doubt.  If someone's an NO Catholic, there's an extremely high degree of "suspicion" that they're heretics, since the vast majority of them are, but that suspicion alone doesn't suffice to exclude them from the Church.

Would I pray with Jorge Bergoglio?  No, absolutely not.  But I'd have no issue, say, praying a Rosary in common with a group of Conciliar Catholics, with the Rosary being almost a shibboleth indicating that they still have the faith.

Some of that depends on the context as well.  I would pray with them privately, but I would never go into their church and join some kind of NO prayer service, because, as a group, and as an institution, it's true that the Conciliar Church is not the Catholic Church.

So what you're saying is: you'll pray with the followers of the conciliar church but not the leaders?

I argue that Jorge is NOT in the Church. How could he be the earthly leader of the Church to which he does not belong?

https://judaism.is/jorge.html 

He is just "subsisting in" the Chair of Peter. 

Looks like it makes sense at the first look, but you can basically use the same logic for literally any heretics, or at least the followers of a heresy if not the inventors? Most likely they probably don't know the truth instead of knowing but denying.

You asked if praying with NO/Vat2 Catholics amounted to heresy. I gave you my answer, which is NO. Other people have said so in various charitable ways.

So what is the heresy that you speak of? It is the hierarchy of the Catholic Church which decides. In the meantime we do our best with what we have and what we haven't. It is not a simple laywoman, no matter how zealous she may be, who defines heresy. As much as you feel, as a neophyte, that you know best, you should learn to eat humble pie and learn from mature Catholics. 

They have not been formally condemned as a group to be heretics, so no. The people making up the NO are at worst material heretics.

Now, if you know individuals who are formal heretics, by all means avoid praying with them.

That goes for ALL people, trads included, family included.

Yet it's ok to say Pope Francis is a heretic? Hmm...

You wrote this in response to Josefa who said nothing about Pope Francis. I don't recall anyone else saying that either, at least on this thread. Be careful of putting words in another's mouth. 

Indeed it's confusing. If people can use the terms like "post-conciliar church" as if it's another church or say it's a new religion, meanwhile I'm getting scolded for making sure if I can pray with them. Also how is it they're not formal heretics, so praying with them in private - OK, but you can say a Pope or some clergyman is a heretic, yet not formal heretic, but praying with them - not OK.

I'll say it again, this time s l o w l y and LARGER.

A – h e r e t i c – c a n n o t – b e – a – P o p e.

Get the memo.

Indeed it's confusing. If people can use the terms like "post-conciliar church" as if it's another church or say it's a new religion, meanwhile I'm getting scolded for making sure if I can pray with them. Also how is it they're not formal heretics, so praying with them in private - OK, but you can say a Pope or some clergyman is a heretic, yet not formal heretic, but praying with them - not OK.

Pope question aside, you really need to read Abp. Lefebvre's "An Open Letter to Confused Catholics", "I Accuse the Council!" and "Against the Heretics" to understand WHY we refer to it as a "post-conciliar church"

As for heretical clergy vs laity, the clergy are public figures and speak publicly on matters of the Faith. When they are out there saying things like "all men can be saved" or promoting sodomy or that divorced and remarried couples can receive Communion., then you have a serious problem with formal heresy.

Which is an entirely different problem than the poorly-catechised Novus Ordo friends you pray the rosary with who may or may not know that Extra Ecclesia non Salus is a Dogma of the Church and that their "nice" Evangelical, Muslim or Jєωιѕн friends will go to Hell if they do not convert.