For me personally, I don't really care how or who defines a religion.
I think you do care though, particularly if someone who isn't a Hindu defines your religion incorrectly. I care about how someone defines my religion too. However Baha'is are arguably more outward looking so are naturally interested in the global community as a whole, religion, history, science, and even politics. So it matters to us that other religions are presented fairly and we certainly don't want to be the one's misrepresenting other religions. That doesn't mean we don't have something to say about them.
If the Baha'i' want to define themselves as a religion, so be it. If others don't want to, that's fine too. As an outsider, it matters not, but I can understand how it would be important to Baha'i, as it adds legitimacy on the world stage.
We want to fair about how we define ourselves too. Abrahamic and world religion. That's relatively easy.
Being the fulfilment of prophecies of other world religions. That's where it gets interesting...lol
Hinduism is often though of as vast enough to be 4 religions: Saivism, Shaktism, Vaishnavism, and Smartism. Some people divide it up differently, but that's mostly used as a way describing the diversity of belief within the umbrella, and it often, in terms of diversity is considered by Hindus as roughly the equivalent of Abrahamism. 'Hindu' is an outsiders word, not our own. Still, most Hindus are sort of comfortable with the term and the misconceptions outsiders have of our diversity.
That all makes sense and resonates with the little I know.