@Amanda1069 Hosts are divided on this issue. There are some who feel entitled to enter and turn off lights, turn down AC or heat, etc, because if guests leave them on when they're not home, some really unattentive and disrespectful guests can actually run up a utility bill that's higher than the profit the host is making on the booking. Not to mention that we all need to be mindful of unnecessary waste of resources because of the environmental impact. And if a host sees the front door left open, with no one there, of course that's a huge security issue, for both host and guests.
But generally speaking, guests are entitled to feel that the space they booked will be private for the course of their stay (unless the host has made it clear in the listing that they go in once a week to clean and change bedding, for instance, or there's a emergency situation, like flooding or a fire), regardless of whether it's a private room in the host's home or an entire place. I never go in my guests' private room unless they ask me to for some reason, but once I went in when the windows were left open and it started to rain hard. I texted the guest to let her know I was going to do that.
In the situation you experienced, I think @Emilia42's suggestion is good- message the host and apologize for leaving the door open and the AC on, explain that you had just stepped out for a quick shop, that you'll be mindful in the future, and let them know that them coming in when you weren't there made you uncomfortable. Good, polite, honest communication between hosts and guests can solve a lot of issues without them turning into some major source of contention.
You can rest assured that the majority of hosts, even if they feel the need to go in for some reason, will just take care of business, they aren't interested in snooping through your stuff or anything like that. But I do well understand that it can feel like a violation.
