I disagree, autopilot can be used in relative safety (nothing in Eve is absolutely safe when you're not docked). You just have to be smart about when, where and how you use autopilot.
First off if you're under wardec or you're a criminal then flying on autopilot isn't safe at all so don't use it. Not at all. If someone has kill rights on you that could be just as bad but it's not certain trouble like a wardec or criminal status is.
Assuming the above does not apply to you, you can use autopilot with reasonable safety in hi sec.
NEVER, EVER USE AUTO IN LOW OR NULL.
Using auto in low/null is just asking for trouble. If you're lucky you might get away with it for a few jumps but it probably won't be long before you run into someone and then you're dead..
ONLY USE AUTOPILOT IN HI SEC.
Unless otherwise specified, everything after this point assumes a pilot flying in hi sec only. A pilot who is not under wardec, is not a criminal and hasn't given other players reason to hunt/grief/harass him personally.
If you're carrying valuable cargo, especially in a big slow ship, you should use manual piloting instead. Even in hi sec and particularly on the last jump into a major market hub.
How much does your cargo need to be worth before using autopilot becomes too risky?
That depends really.
Leaving aside the rare crazy suicide ganker and anyone with a personal vendetta against you, most gankers are in it to make a profit or at least cover their losses. Most will ignore anything worth under 200 mil and many won't bother with anything less than 500 mil. However that doesn't mean some won't go after targets worth less. It all comes down to if ganking you pays well enough to replace the ship(s) they need to kill you before Concord kills them. If the math doesn't work out in their favor they'll leave you alone.
What you're flying makes a difference too.
Your ship's fittings and salvage value make a difference, the more valuable stuff your ship is likely to drop the more attractive a target it makes. Your ship's tank also matters, the better tank you have the more ships and/or more valuable ships it takes to kill you.
The usual targets are big slow hauling ships gankers can take their time scanning and easily overtake if the cargo (or cargo + salvage) is valued over the threshold they consider worthwhile. I only use small, fast T1 frigates and Cov Ops frigates for my transport needs. I don't deal in anything bulky enough to require anything bigger to move it.
As far as I can tell most gankers don't seem to bother scanning frigates very much at all. They probably figure frigates don't carry anything valuable enough and aren't worth the time. Or maybe it's something else. Whatever, I know I hardly ever get scanned anyhow. I used to pilot manually whenever I had much more than about 200 million onboard but the last few months I'm pretty much always on auto unless I'm carrying cargo worth 500 million or more.
I've been playing EVE for nearly a year now. I have 10 trading characters all of which have at one time or another used autopilot extensively while working regional trade all over empire space. In that time exactly one character has been ganked just once while on autopilot in hi sec.
That's an acceptable risk to me, in fact it's better than acceptable, it's negligible.
Industrials and other big, slow hauling ships can be auto-piloted safely enough too though not as safely as frigates. Big haulers are primary targets for ganking, not only do they attract more attention and get scanned more often than frigates, but they're slower and take longer to align and jump too. Don't forget to tank that hauler, a poorly tanked hauler makes a terrific target for gankers flying cheaper, less powerful ships than usual.
Just how much less safe auto-piloting big haulers is I'm not really sure. When I first started playing I never had any trouble auto-piloting Badgers and Badger IIs all over empire space (not in hi sec anyhow) but I never carried much more than about 10 million in them and my Badgers were very heavily tanked too.
A little trick that speeds things up slightly is to make the first jump manually and turn on autopilot as soon as your ship enters warp. It'll warp directly to the first gate and jump immediately saving you the approach time.
Where autopilot really comes in handy is when running 2 or more clients at once. I often pickup filled buy orders on 2 or 3 characters at the same time and I'm usually either afk or semi-afk while doing pickups (I'm semi-afk while writing this right now). I like to tab back and forth between characters occasionally and hit the MWD to speed up gate/station approaches. If I notice suspicious ships around a character, I'll turn auto off, do a jump or two manually, then go back on auto.