A perspective from the other side.
At our clinic, first appointments are at 8.30am. We will typically be there from 8am, and will take phone calls from then. However, we often have discussions relating to confidential information and workload for the day at the reception desk prior to opening time (yes, it needs to be at the desk, where all the info is). Thus, the doors don't open until 8.25am so we can be properly organised for the day. It's obvious we're in the clinic, but we need this time prior to opening, uninterrupted by dealing with patients walking in. Same goes for appointments after lunch break. Again, ongoing discussions are held prior to afternoon session, so doors will not open until just before 2pm.
Previously, we didn't lock the doors, and would have patients simply come in early (some, up to 45 minutes early during our lunchbreak!) as they were "in town, and finished their other tasks". When we mentioned that we were still on break, and attending to other tasks ("lunchbreak" not necessarily meaning we weren't actually working, just not available for patients coming in), the common reply was "Oh, that's okay, I don't mind waiting". Not a good thing, as it threw our schedule out, and meant we couldn't discuss sensitive information. Plus, at times we actually liked to get a "break" if possible!
So please realise that while it may be convenient for you to arrive quite early, there are other tasks the staff may need to do in private, without patients around. We found that allowing patients in to wait in the above cases meant they wanted to "chat" (or worse, actually be seen extremely early) and we couldn't get anything else done. We are a friendly clinic, so it's lovely our patients like to spend time with us, but lines do need to be drawn.