For the keyboard / mouse control scheme, left-click selects a target and right-click both selects and auto-engages. Unfortunately, particularly when tired, hitting the right mouse button by accident is a real possibility, especially if one's hand is returning to the mouse after, say, typing in preparation for an S-rank (I've seen friends do this, and they always feel miserable afterward).
The Tab key can also be used to target monsters. However, whether it auto-attacks or not depends upon whether a character is currently engaged. If I'm standing around minding my own business, I can tab through everything, no problem. If, however, I'm engaged with one monster (say in a FATE), and then Tab over a random bystander critter on my way over to the next FATE enemy, there's a good chance I'll shoot it (and, if I'm in a group with a friend or two, likely link a few other monsters in the process given FFXIV's asinine monster-linking rules). This scenario occurs quite routinely in solo content, for me at least; FATEs, Levequests, whatever - anything where I'm only wanting to target certain monsters out of a group. It essentially eliminates my ability to use the Tab key, forcing me instead to manually select the monster with the mouse, which can get tricky if they're moving around (monster selection boxes aren't as well-designed as they could be).
Again, for any other job in the game besides BRD and MCH, there is no risk to these types of activities. Accidentally hit the right mouse button? Tab over the monster? Whatever - unless you're right next to it, auto-attack might "engage", but it won't do anything. That's the way it should be for everyone. Auto-attack simply shouldn't be capable of initiating combat itself with a previously un-engaged enemy.
Edit: One other complicating factor when using the mouse for targeting is that the mouse also controls my camera, and influences my movement. Occupying it briefly to select an enemy interrupts this, which can (and does) have an impact on AoE avoidance, for example. I'm not sure how typical keyboard / mouse users play, but I know for me, avoiding an AoE with the keyboard alone feels very unnatural; I typically use the mouse to ensure that I am running in an optimal direction and maintaining optimal camera positioning. Granted, this isn't terribly important in solo content like FATEs or Levequests, but it's ingrained in me from higher-tier content.