If you want to say Islam denies Christ and therefore doesn't worship the same God, then we ALSO must conclude that Jews don't worship the same God. Muslims at least consider Him a prophet, Jews consider Him a deluded heretic, so there's even less justification for saying Jews worship the same God.
But, since Jesus said "salvation is from the Jews", that conclusion creates theological problems that cannot be resolved.
God is All-Just, All-Merciful
Jesus and Mary are sinless.
Jesus was born of the Virgin Mary.
Jesus is judge on the Last Day.
These are all Muslim beliefs.
Islam is just another Protestant heresy. Islam uses an essentially Eastern approach to understanding God, but without the Catholic leaven of sacraments and liturgy, Islam makes mistakes just as heinous as the Western Protestant approach. Indeed, viewed in this light, the rise of Islam could easily be seen as the Eastern Catholic version of the Protestant Reformation.
When I taught RCIA, I used to point out that people who only understood addition and subtraction are not denying math, they are merely ignorant of the higher forms of math. When it came to theology, the pagans know the four basic operations (addition, subtraction, multiplication and division), but not much else. The Muslims understand algebra, but have no grasp beyond that. The Jews, the Chosen People, understand geometry. Non-Catholic Christians can get through most of trigonometry without too much trouble. And non-Catholic liturgical Christians, such as the Eastern Orthodox or the Coptics, even manage single-variable calculus. But if you want to understand the whole width and breadth and height of the subject, only the Catholic Faith will do.
Now, none of these groups are totally wrong. It's just that only one group has a really thorough, comprehensive understanding. Our job is not to deride them for what they do not know, but rather to teach them. Cardinal Burke has, for whatever reason, lost sight of how it all works.
This interesting analysis from Ross Douthat points out the problem:
"Cardinal Raymond Burke, gave an interview suggesting that papal silence might require a “formal act of correction” from the cardinals — something without obvious precedent in Catholic history."That sounds exactly like the New Age lefties after VC II (and I include Lefebvre in that list of New Age Lefties), inventing new "precedents" in order to accommodate their personal schisms and heresies. That single sentence from Douthat really tells you all you need to know about the "traditionalist" Cardinal Raymond Burke.