Well, I’m not a Catholic (in full communion with Rome, that is), let alone a Catholic apologist. So definitely take this as speculation. But I don’t see why God wouldn’t reveal Himself to a sincerely seeking person from another religion. Of course all experience of God is going to be interpreted through the lens with which we are familiar. As Christians we believe that God has given us the right lens. But that doesn’t mean that Jews and Muslims are not experiencing the True God.
And on the whole Jewish and Muslim mystics tend to sound more like Christians than non-mystical Jews and Muslims do. In other words, in both religions the mystical experience of God leads to a more immanent understanding of God as someone who loves us and relates to us intimately, not just someone who is a far-off King and Judge (granted that I’m probably being unfair to non-mystical Judaism and Islam in characterizing it this way).
Here are a couple of examples from one of my favorite Muslim mystics, Rabi’a:
Your hope in my heart is the rarest treasure
Your Name on my tongue is the sweetest word
My choicest hours
Are the hours I spend with You –
O Allah, I can’t live in this world
Without remembering You–
How can I endure the next world
Without seeing Your face?
I am a stranger in Your country
And lonely among Your worshippers:
This is the substance of my complaint."
My peace, O my brothers and sisters, is my solitude,
And my Beloved is with me always,
For His love I can find no substitute,
And His love is the test for me among mortal beings,
Whenever His Beauty I may contemplate,
He is my “mihrab”, towards Him is my “qiblah”
If I die of love, before completing satisfaction,
Alas, for my anxiety in the world, alas for my distress,
O Healer (of souls) the heart feeds upon its desire,
The striving after union with Thee has healed my soul,
O my Joy and my Life abidingly,
You were the source of my life and from Thee also came my ecstasy.
I have separated myself from all created beings,
My hope is for union with Thee, for that is the goal of my desire.