Any religion has two functions
1. To keep fabric of society intact by changing the way people live in the society according to the changing times. This includes changes in external appearance such as houses, dresses, communication means, transportation, technology adoption and so on. Religion should thrive on logic and not on sword.
Any religion loses its utility when it perpetrates injustice in the name of religion or preaches killings, woman mistreatment and so on. Religion must maintain peace in the society which is utmost essential for anyone who wants to stay in the society and take a spiritual path. 2. To suggest ways and means for purification of mind to achieve the supreme goal of uninterrupted happiness. Let us take a case of Hindu religion

Hindu religion has undergone many changes in both the aspects. Over the years many Saints allowed changes in external appearance maintaining that God does not go by what you wear but He goes by what you think. Therefore most of hindus wear western style dresses yet undertake devotional practices.

Regarding the second point
Earlier there were reference to penance then to rituals then to worship and now in this age to Bhakti (Devotion).
If we see the history since emperor Ashoka...
Buddha rectified wrong and cruel practices of then hindu people by Rejecting the hindu religion it self. At that time people were used to quote Vedas and other scripture to support their killings, drinking wine. Even it was said that wars were must for a king. With this kind of philosophy people could not live peacefully. Buddha decided to reject Hinduism itself even though He was one of the descendants of Bhagwan Vishnu as no amount logic would stop the prevalent malpractices. The need of that time was ..."Complete Nonviolence..Ahinsa Paramo Dharmaha"

Then came Shankaracharya... seeing that ground ready to relaunch the Hinduism, he defeated buddhism Nirvana by sheer logic using similar philosophy of Adwait (which says God and soul are the one) and brought back hinduism in India.

Then came saints who preached Bhakti along with rituals.
And today 99.99% fake saints are in the market, Atmosphere is full of material attractions, Money has taken the center place, corrupt ways to earn are rampant. With this background all rituals are meaningless. They cannot bring you the spiritual upliftment.
Hence many saints from Tulsidas to most recent Jagadguru shriKripaluji Maharaj emphasized only one thing...Remeber Him and Love Him ...Nothing else is essential..Your faith, your cast, your nation, your language, does not count. What you wear does not count. Rituals are hindering blocks.

Love that matters. In this age everyone talks of love and love is prevalent everywhere. Thus way to God through Love is the most befitting philosophy to purify mind in this age.
Hence Hinduism was not outdated religion at any point of time in the history. This the only reason it survived in India, though India was ruled for many years by Muslim Kings and then by the British.