The most common one - Hinduism is not a religion
Religion is a western term. Hinduism is Sanatana Dharma. This is covered in the next point. For this point, please note that when we talk of religion, we usually refer to Abrahamic religion. Religion, according to this paradigm, is generally understood to have the following characteristics :
Has a specific prescriptive model of God
Has very prescriptive DOs and DON'Ts
Usually has an identifiable founder
Threatens potential transgressors with hell
Usually aggressively conquering / proselytizing
Has one main scripture with subsidiaries
Has well defined, unvarying rites and rituals
I am not saying all of Abrahamic religions are like this, but these points are generally associated with the term "religion".
Hinduism has none of the above characteristics. Some treat Maa Shakti as greatest, some as Vishnu, etc. Some believe in rituals, some treat God as formless, some prefer Vedas, some Gita and so on. So in this paradigm, Hinduism is not a religion - this is the common case.
Hinduism as a religion :
Now if we take the correct definition of religion as on wiki - Religion, Hinduism would be considered as a Dharmic religion. Although the origin of the word "Hinduism" is debatable, its a well known fact that it is called as Sanatana Dharma since ancient times. Sanatana means eternal and Dharma refers to Laws and duties of an individual that are necessary to maintain harmony in the universe.
So according to the universal definition, which is the correct one that we should consider, Hinduism is a religion.
Hinduism as a way of life - clearing a common misconception:
Sure, Hinduism is a way of life. But so are all the religions, Abrahamic or otherwise. Many people incorrectly think that Hinduism is not a religion because it is a way of life, or Hinduism is a way of life because it is not a religion. This is a misconception. Every religion prescribe certain customs, beliefs, etc that people adopt in their day-to-day life. The difference in Hinduism is that it does not prescribe specific customs or beliefs. It's a philosophy on decentralized paradigm where individuals can choose to follow what they like.
Hinduism as an open-source religion :
Now they are millions of Gods, thousands of scriptures, uncountably many beliefs, etc under the umbrella "Hinduism". People are free to choose whom they pray, what they study and follow, etc. Not only this, people can pick any "version" and extend and customize it according to the needs of the hour, ie. it keeps on getting "refreshed", otherwise it would have become obsolete. Swami Vivekananda, Chaitanya, etc - all of them popularized different schools of thoughts. So in this sense Hinduism is called an open-source religion. But a very important distinction from open-source softwares is that the core values of Hinduism like concepts of Karma, Yoga, Dharma, Moksha, universal peace, etc remain the same and so does the core messages of the scriptures.
OM
Vasudeva Kutumbakam