I am sharing some Hindu beliefs that I personally find significant. Though these beliefs are popular, I would not like to impose them on all Hindus.
Existence of Truth
Hindus believe in the existence of a supreme reality. For most, this refers to the Divine — Rama, Shiva, or Durga. For the atheistic, this could refer to supporting the notion that goodness is a better option in life than hurting anyone. After all, the actual word for Hinduism is “Sanatana Dharma,” which means Eternal Righteousness.
Multiplicity of paths
Hindus believe that there is more than one way to approach the ultimate reality and therefore respect alternate viewpoints. They understand that more than one right answer may exist for every question. This aids in maintaining the dynamic nature of Hinduism.
Just like beings can amend the constitution in a democracy, the knowledgebase of Hinduism can be updated. This does not mean that anyone can write a new Upanishad. It means that we can become a Brahman-rishi or a bhakti saint one day and then write a new Purana or Upanishad.
Because of Hinduism’s adaptability, every vote, including that of the unrealized, counts in Hinduism. Because every viewpoint has some lesson, it is worth listening to, though we do not have to follow it.
Liberation for all
Freedom is a property of the soul; every being deserves it and eventually reaches a state of total bliss. This is the final aim of life in Hinduism.
Everything other than the Divine and his name is perishable or less permanent.
Sita-Rama, the queen and king of the universe, the Bhavani-Shiva, our divine parents, continuously observe our actions, including the intention with which they are performed. Saying “sorry” for our bad karma may wash away some of our karma, but we still have to change ourselves to reach bliss.
Hindus believe in the existence of grace (kripa), but even the best saints and philosophers of Hinduism do not quite understand how the grace of Rama works. So I’ll stop here as well.
Bhakti and realization are independent of philosophy. If we like a specific philosophy or Vedantic commentary and want to use it on our path to God, we can. But all theories are optional; they are not necessary for reaching God.