Reply:  They believed things differently back then and things have changed now with a different understanding.  smh

This is precisely why it’s useless to argue with this person. It seems to me that this person doesn’t profess the True Faith. 

3039 Dz 1818 3. “If anyone shall have said that it is possible that to the dogmas declared by the Church a meaning must sometimes be attributed according to the progress of science, different from that which the Church has understood and understands: let him be anathema” [cf. n.1800]

Muslims are hypocrites. They claim Christ is the greatest prophet, yet they don't believe in what Christ said and instead follow mohammet.

I would give them some credit, naturally speaking.  When the Jєωs aired a TV show that was blasphemous against Christ, the Muslims were rioting because it was insulting to their prophet, while the Christians did nothing.

Vatican I taught that the existence of God and his natural "attributes" are knowable by natural reason.  But actual supernatural faith (aka "belief") entails knowing something (i.e. has for its object) those truths which can ONLY be known by Revelation.  So, to claim that Muslims "believe" in God would be to deny both these aspects of Vatican I.

No, they have simply made (sometimes accurate) conclusions about God as He can be known from nature through human reason, but they do not believe in Him because they do not believe that which He has revealed about Himself.

This actually summarizes all the putridness that is Vatican II.  V2 concludes that these false religions believe in God and worship Him simply because they have MATERIALLY come to some of the same conclusions about Him.  But that is false.  In order to have belief, one must actually believe these things based on the correct formal motive, i.e. the authority of God Revealing as made know to us through His Church.  This is why a heretic who believes every single teaching of the Church except one is said to "believe" NONE of them.  So the 99.9% of what he holds to be true, while materially correct, are not believed for the right reasons, through the proper formal motive.  If a Prot concludes some true things about Christ from the Bible, he doesn't believe those things, since He doesn't believe them based on the authority of God Revealing but based on his own interpretation (so that his own interpretation becomes his rule of faith ... cf. St. Thomas on this point.).  This, BTW, is the very same error that +Fellay makes in characterizing V2 as "95% Catholic".  There's no 95% Catholic.  There's no 99.9999% Catholic.  Simply because, numerically speaking, 95% of the propositions in Vatican II are materially Catholic, the are all formally polluted by the context in which they are presented.  OK, sure, V2 might affirm the Holy Trinity.  But HOW do they affirm the Holy Trinity and in what context?  They present the Holy Trinity as merely the "fullness" of truth on a sliding scale from less true to more true.  That context undermines even their affirmation of the Holy Trinity because the context renders it effectively to be an optional belief that's the "full" truth vs. presenting it as THE truth that's opposed to all the errors about it.  This context formally pollutes all of the materially-correct propositions in V2.

V2 subjectives the notion of "formal" motive.  For V2, wanting to know God has become the new "formal motive" of belief.  Simply because you have a subjective desire to know God, this means that you have the proper formal motive.  But formal motive is actually.  It does not refer to your "sincerity" but, rather, to whether you belief what you believe for the objectively right motives, i.e. with the correct rule of faith, the rule of faith being the formal motive for belief.  This is an objective thing and not to be confused with "sincerity" or "good intentions".  So, a Prot can be perfectly sincere in his beliefs and properly motivated (most aren't, but let's assume that one is for the sake of illustration).  This still does not equate to the proper formal motive of belief, which is that we believe what we believe BECAUSE of the Church's authority to interpret Revelation.  Prots do not base their (natural) beliefs on the correct formal motive, and they can be as sincere as all getout, but this does not equate to the proper formal motive of faith.  This trend to re-interpret "formal" into "sincere" has been ongoing since the 1500s, and it's what led inexorably to Vatican II.

So these are the two critical distinctions in play here, and these statements by the person cited by OP epitomize the V2 apostasy.

1) Natural Knowledge vs. Supernatural Belief
2) Materially-Correct Propositions vs. Formally-Correct Propositions

Believing in the Supreme Being is natural knowledge and not belief of any kind.

Having come to some materially correct propositions about God does not equate to formally-correct "belief".

Traditional Catholics who are hostile to the EENS aspects of "Feeneyism" (prescinding from any discussion of BoD per se) demonstrate that they have been polluted with this same erroneous mindset.  They hold to this notion of salvation by sincerity, that someone who means well can have the proper formal motive of faith and therefore can be formally Catholic.  This is radically false and is the core error behind all of Vatican II.  SINCERITY DOES NOT EQUAL FORMAL MOTIVE OF FAITH.  Formal Motive of faith refers to an objective reality where I believe the truths revealed by God on the authority of God revealing through His Church.  As St. Thomas taught, just because you CLAIM to believe something on the "authority" of the Bible, for instance, this does not equate to having the proper formal rule of faith, since in the final analysis, your own mind, your own interpretation are your rule of faith.  While claiming that their beliefs are rooted in the authority of God, they're really not.  This comes from the 500-year progression of warping the term "FORMAL" into a subjective sincerity rather than as the description of your objective motivations for belief.

The weird thing is that Muslims and Jєωs are actually more correct on this than Vatican II. You can tell your friend this.

When asked if they believe in the same God as Christians, the answer is no. I have no idea how V2 managed to flub that up so badly, maybe they were all high on drugs.

Similarly, the Novus Ordo will give "Communion" to Eastern Orthodox, whereas the Orthodox will refuse Catholics the same.

So I'm in an online discussion with a lady about how the Catechism/Lumen Gentium declares that we worship the same god as Muslims.  Here is what she said:

"Of course we worship the same God as the Muslims! They just don't worship Him in His fullness that is the Trinity. There's only One God so as long as you worship God and not Satan you are still worshipping God, even as imperfect as that understanding may be. Your responsibility as a Catholic is always to construe the Catechism in the way the Church construes it, not in the way YOU construe, lest you be in error."

How would you respond to her?

This is a thoroughly Modernist statement.