That doesn't mean they are perfect, but they are certainly Catholic.

Rubbish. There you go again with your non-existent charism of reading hearts, minds, and souls to create yet another straw man.

Quote any sedevacantist who has said, "the conciliar church and its adherents are beyond all hope."

Precisely because we do have hope, every sedevacantist I know prays for the conciliar sect, just not with the conciliar sect.

Your thinking is sloppy, if indeed you think at all.

Rubbish. There you go again with your non-existent charism of reading hearts, minds, and souls to create yet another straw man.

Quote any sedevacantist who has said, "the conciliar church and its adherents are beyond all hope."

Precisely because we do have hope, every sedevacantist I know prays for the conciliar sect, just not with the conciliar sect.

Your thinking is sloppy, if indeed you think at all.

You might "keep in mind" a fundamental truth: You cannot read hearts, minds, and souls.
So stop projecting your noisome imaginings upon others, give up your straw men, and stick with objective truths, verifiable verbatim quotes, rationality and logic, and demonstrable facts.
Is your question intended as an insult? Of course God hears all prayers.

That's not what I said at all.  Not even close.  

For Traditionalists are 100% orthodox and, assuming they are in grace, have their priorities straight.  

When one is in mortal sin, all of one's prayers are not beneficial in the same way that one in the state of grace's prayers are.  God still hears all prayers, but since He is PRIMARILY concerned with the salvation of our souls (and we, mostly, are not...and certainly the person is mortal sin is not concerned with salvation), thus He uses our prayers PRIMARILY to help us convert, to go to confession and to get back in the state of grace.  It's like if a person were starving, yet they were praying for tickets to a music concert.  God would not hear the latter prayer, and He would use those prayers to provide them with the basics first - food or conversion.
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In the same way, the vast majority (98%) of novus ordo catholics are not orthodox, not living the Faith and not concerned with salvation, as they should be.  The 2% others may be "conservative" but they are still stuck in the mire of the indult thinking, which is not totally orthodox, so they need conversion too.  Whether or not you can say that new catholics have "faith" depends on how you define "faith" (something which +Williamson never did and which is problematic because his statement is too ambiguous).
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So does God hear the prayers of the novus ordo catholic in the same way that He hears those of Traditionalists (presuming the Traditionalist in question is in the state of grace)?  No, He does not.  For Traditionalists are 100% orthodox and, assuming they are in grace, have their priorities straight.  While those in the novus ordo need to convert in some way, so God prioritizes their prayers for their conversion first, with all other things as being superficial.  As the Gospel today stated, "Seek first the Kingdom of God...and all else will be given to you."  Those in the novus ordo do NOT seek FIRST the kingdom of God, as they seek first the kingdom of rome, and of the pope, with the True Faith being a secondary priority.