The word Hindu in American English

I, as an Indian, am often surprised when the Americans use the word Hindu, when they actually mean

1. The country of India


2. The Indian subcontinent


3. The Hindi language (possibly)

whereas it should only refer to the Hindu religion, or Hinduism.

For example, there is the Hindu-German conspiracy of 1915. While most of the Indian conspirators may have been Hindu, it does not appear to have been religiously motivated.

An American cousin of mine wanted a 'Hindu Barbie' in a sari. It sounded inaccurate, at least to my years. Occasionally, I have heard an Indian accent being referred to as a 'Hindu accent'. To my ear, this sounds as ridiculous as an accent being referred to as, say, a Catholic accent, a Baptist accent, or a Jewish accent.

The British do not usually do this, but I did see an old (1930s) film where the actor claimed that a nonsense word was 'Hindu' for welcome.

What is the reason for this usage? I did hear one possible explanation. A friend of mine visiting South America took exception to this usage. Upon enquiring, he was told that the word 'Hindu' refers to 'Indian Indians', while 'Indian' refers to native South Americans.

Was this the case in the USA as well?

How common is this usage? Is it universal, or only among the poorly educated? Why don't people say South Asian, or Indian, or the subcontinent, depending on the context?

To be fair to the Americans, the words and phrases Hindu, Hinduism, India, Indus, Sindh, Sindhu, Hindi, Hindostan, Hindu Kush, etc all have the same origin.

However, non-Hindu South Asians, including Indians, and even some secular Hindus may be offended by such usage.