In Battlegrounds, I always close the door behind me. It's not a matter of strategy so much as it's a psychological thing — it makes me feel safe. The house I've entered is a safe, isolated little haven full of goodies just for me, and nobody, ever, will come up behind me and shoot me in the head.
That's not the way everyone does it, and I'm well aware that my habitual door-closing is just to trick myself into feeling less scared. Better players than I will systematically leave doors open to ward off opponents — it's a small way of hinting to others that a house has been looted and there's nothing for potential aggressors to gain by entering.
There are an infinite number of ways to approach doors in Battlegrounds. If there are ten players left, you might close one door to a house and leave another open, creating a false pathway where you might have gone while you're actually crouching in the bathroom, waiting. If it's early on in the game and you only have a machete, perhaps you wouldn't spend the extra second closing a door instead of searching for better weapons.
What are your door-closing habits in Battlegrounds?