Can I keep my beard?

Hi everyone. I'm a 23 y/o South African born Indian man visiting india for the first time within the next week. I've been advised by 2 relatives to shave (or greatly reduce the size of) my beard. Over the last few years, I've maintained a well-groomed beard, which I've adopted very much as my physical appearance. If anything, I'd feel uncomfortable without it. My relatives said I should remove my beard, as they claimed that I could be putting myself at risk by being mistaken for a Muslim. They said I could be subject to more scrutiny by police and locals and could possibly get myself into unnecessary trouble. In no way, shape or form am I trying to be racist, xenophobic, bigoted, prejudiced or discriminatory to anyone. I find my relatives sentiments hard to believe, and I prefer to take things like this with a pinch of salt. Hence, I want to find out whether there is any truth to their beliefs. I would like my first visit to India to be as smooth, memorable and sweet as possible. edit: might be good to add that a majority of my trip will be spent outside of cities and towns, mostly in rural areas and visiting temples/other religious sites across India.