The "modern" sages of the Advaita are part of the Traditionalist School: for them, the other religions are other valid paths to the Absolute.
I will quote from Sri Râmakrishna to illustrate this position:
He who is called Krishna is also called Siva, and bears the name of the Primal Energy, Jesus, and Allah as well--the same Rama with a thousand names. A lake has several ghats. At one the Hindus take water in pitchers and call it 'jal'; at another the Mussalmans take water in leather bags and call 'pani'. At a third the Christians call it 'water'. Can we imagine that it is not 'jal' but only 'pani' or 'water'? How ridiculous! The substance is One under different names, and everyone is seeking the same substance; only climate, temperament, and name create differences. Let each man follow his own path. If he sincerely and ardently wishes to know God, peace be unto him! He will surely realize Him.
- Gospel of Sri Ramakrishna
This verse is often cited as an example:
Gîtâ IV.11: In whatsoever way men approach Me, even so do I reward them; for it is My path, O Partha, that men follow in all things.
However, we can read in the Manusmṛti:
12.95: All those traditions (smriti) and those despicable systems of philosophy, which are not based on the Veda, produce no reward after death; for they are declared to be founded on Darkness.
12.96: All those (doctrines), differing from the (Veda), which spring up and (soon) perish, are worthless and false, because they are of modern date
How can this apparent contradiction be resolved? Should we reject Manusmṛti because it is not a Śruti? Or on the contrary, reject the opinion of "modern" gurus? What is the opinion of the Vedas and Adi Shankara on this issue?