There are many non-Hindus converting to Hinduism and nobody has a caste. Hinduism is not rigid. It has undergone several changes and scriptures keep getting updated and newer ones are added.Every scripture sir. Now you can try and put a modern twist on how varna are not to be taken literally. Bhagwad Gita clearly tells how karma dictate what caste , animal or gender a person is born as. A person's duties are determined by his or her caste and status.
Don't worry all religions put their modern twist to keep themselves relevant.
Most of the Hindu scriptures are written down only in the last 1000 years. Prior to that they are all orally transmitted. Hinduism as we see today is pretty young. Younger than Islam. It is Brahminism. A marriage between old Vedic religion and mainland Indian local beliefs with many principles of Buddhism and Jainism incorporated in it.
Hinduism can be updated and modified unlike Abrahamic religions which are immutable. There is a space for everything in Hinduism. Its just an umbrella term for thousands of local beliefs in India.