No. Not Brahmins, but Mahatmas, saints, sages and Avatara Purushas are indeed the saviors of Hinduism. These great souls come from all castes and all walks of life. Incidentally, some of them are Brahmins.
In a way, Brahmins are better positioned to become mahatmas, saints and sages, because of the way of their upbringing, cultural background and tradition, their self-discipline, their intellect, their better exposure to core scriptures and Sanskrit. But positioning alone does not assure becoming.
Non-Brahmin saints & Sages:
Avatars of Vishnu — Sri Rama and Sri Krishna were kshatriyas. Many of the sants of Maharashtra’s Varkari Sampradaya were non-brahmins. Meera Bhai was a kshatriya.
Several Azhvars of Tamil Vaishnava Bhakti tradition were non-brahmins. Most of the 63 Nayanmars of Tamil Saiva Bhakti tradition were non-brahmins. Vallalar Sri Ramalinga Adigalar (Tamil Nadu) was a non-brahmin. Nandanar (Tamil Nadu) was born in scheduled caste. Most of 18 Siddhas of Tamil Nadu were non-brahmins.
Kabirdas was a Muslim. Rayidas was a cobbler. Sri Satya Sai was a Kshatriya Raju by birth, Swami Vivekananda was a Kayastha (non-brahmin) by birth.
Akka Mahadevi (Karnataka)
Saint-poets Arunagirinathar and Pattinatthar (Tamil Nadu) were a Vaisyas.
Sri Narayana Guru of Kerala was a Ezhava (non-brahmin). Swami Chinmayananda (Kerala) was a Nair.
Sri Nisarga Datta Maharaj
Mata Amritanandamayi (Amma) (Kerala) is a fisher woman by birth. She has numerous Brahmin disciples.
We also have a long list of saints and sages who were Brahmins by birth.
Brahmin saints & Sages:
Sri Shankara, Sri Ramanuja and Sri Madhvacharya, Swami Desikan, Raghavendra Swami
Samarth Ramdas (Maharashtra), Badrachala Ramadas (Andhra), Papa Ramadas (Anandashram), Saint Thyagaraja Swamigal (Tamil Nadu), Saint Poet Annamacharya (Andra)
Tulasidas, Chaitanya Maha Prabhu, Sri Ramakrishna Paramahamsa and his consort Sri Sarada Devi.
Swami Brahmananda, Swami Shivananda, Swami Ramakrishnananda, Swami Turiyananda, Swami Abhedananda (all of them were main disciples of Sri Ramakrisha Paramahamsa)
Shirdi Sai Baba (Brahmin by birth, brought up by Muslim family)
Bhagwan Ramana Maharshi, Sri Seshadri Swamigal, Kavyakanda Ganapathi Sastri (Sri Ramana’s disciple).
Swami Sivananda Saraswati (Rishikesh), Chattampi Swamigal (Kerala)
Sri Sri Raishankar, Jaggi Vasudev
… and so on.