Hindu is any and every living being (having Atma):
Atma (Spirit) is a part of the Parmatma (God) and all living beings have the Atma (Spirit). The Atma never dies but the body does. Every Atma keeps getting reborn in different forms as the object of the Atma (Spirit) is to purify itself to merge back with the Parmatma (God). Keeping in mind the Karma (act) the Atma does, with the help of its body and mind, it moves (is reborn) from one body form to another and the best earthly form is the human body.
In the human body all have a right to believe in God (Astic) or not believe in God (Nastic). If you believe in God, God can be depicted in lifeless form or with life; formless (Nirakar) or with form (Akar) as:
LIFELESS - Stone
LIFE FORM - Tree/Plant - Bird - Fish - Animal - Human
UNIVERSAL FORM - Sun - Planets - Moon
ELEMENTS - Air - Earth - Water - Space - Fire
Thus in-reality worship in any manner or even no worship is acceptable. Rebirth stops when the Atma (Spirit) merges with Parmatma (God) attaining salvation.
Earlier all persons staying on the east of the Hindu Kush mountains were considered Hindus. However with wars, conquests and migration the status has changed.