Authentic Buddhism does NOT allow you to follow any other religion. Be it the Pali Canon of the Hinayana or the Vaipulya Sutras of the Mahayana or even the Vows of Ambedkar - Buddhists are NOT allowed to practice any other religion alongside Buddhism. Any deviation of this norm to appease secularists goes against the Buddhist sutras.
Throughout history, Buddhists have been persecuted by other religions, and even atheists, in the worst ways -- even bringing Buddhism to total extinction in several nations. Furthermore, Buddhism is essentially and intrinsically different from other religions. To say "use Buddhism to make yourself a better Christian or Muslim or Hindu" is total and complete insanity that propagates an obvious lie that "all religions are the same". No, they are not.
“Buddhists must not believe that Jesus is the only way to salvation, nor should they wash their sins in the blood of Christ - or even believe in sin. Similarly, Buddhists cannot uphold the Hindu caste system of Manusmriti, nor can they endorse the idol-destruction in Islam. To say use Buddhism to make yourself a better Christian or Hindu or Muslim is total and complete insanity.”
Everyone has the right to choose their own religion. But you cannot use Buddhism to make yourself a better Christian -- use the Bible to do so. You cannot use Buddhism to make yourself a better Muslim, use the Koran and Hadiths to do so. Buddhism does not believe in sin or the sacrificial lamb -- and Buddhists do very much practice "idol worship". Buddhism is a separate religion and Buddhists cannot endorse any other religion, period. "Western Buddhists" and those who cater to them, propagate the Hippy nonsense that all religions are the same - but any religious expert will tell you that's not true. The Pope will never say use Christianity to make yourself a better Buddhist -- no Muslim will ever say -- use the Koran to make yourself a better Buddhist. Any Buddhist leader or expert who says one can use Buddhism to make themselves better Christians or Muslims is a fake, a sell-out, an Uncle Tom and a liar.
Be authentic - pledge exclusive allegiance to Buddhism
When dating, you can interact with many partners. But when you marry, you forgo dating and commit exclusively to your one lifetime partner. This is key to a successful marriage and a strong relationship. Similarly, you can study (or flirt) with different religions, but when you choose Buddhism, you must necessary forfeit all other religions.
This is not negotiable and is mandated in the Cardinal Buddhist texts of all traditions. It is also upheld by the greatest Buddhist saints from Shinran and Nichiren to Kumarajiva and Babasab Ambedkar. Let Christians and Muslims do what they must to be "better Christians and Muslims". But a Buddhist CANNOT be a Christian or a Muslim -- Buddhism is NOT an "anything goes, do what you want" religion -- the hippy era of Vietnam is over and Hippy Buddhists will NOT teach Asian Buddhists about Buddhism. Asians, and others interested in following Buddhism, must reference the ACTUAL BUDDHIST TEXTS of their sect -- not the musings of San Francisco hippies or sell-out lamas that distort Buddhism to sell books. Be authentic. Truth Matters. Satyameva Jayate.