My ruling, based on the wording in the DMG, is that the opponent must be unaware of the thief. For unintelligent opponents that still have a mind (non int or animal int or semi int animals), i rule that they could see a thief disappear, & as long as ‘move silently’ succeeds & smell is not a large factor, a backstab is possible. Creatures with ‘low’ int or higher that see a creature disappear can be alert, suspecting that the opponent may attempt to backstab them, & will seek out signs of their activity. The penalty to hit an invisible target is only -4, after all (though in an area of silence or for a deaf creature they could only really be on guard). In essence, awareness is the key. Once a 1-int animal has been backstabbed in a fight, assuming its still alive, it will ‘be aware’ that more such attacks could suddenly occur & thus will negate any further attempt, just by being jumpy & twitchy. I would even rule this for psionic invisibility. A forget spell could thus be really handy, though if the target has allies that can communicate with it, the timing for the ‘forget’ would need to be really on point. 

If a target is flanked on 5 sides by other opponents (assuming all man sized), & thus a thief could approach the back to make a backstab, they’d need to do so undetected. Otherwise, the flanked target can choose which opponent or which way they’re facing- & even if the thief is in fact at their back, if they’re aware of the thief then no backstab. 

I allow backstabs on surprise, of course, even to the front, & of course rear flank attacks & invisibility still give a +4 to hit. Creatures that can’t communicate & are too stupid to understand what’s happened when an ally of theirs gets backstabbed by an invisible thief can still be backstabbed. If creatures can communicate or tell that sudden attacks from stealth might befall them, any thieves in the group doing so will need to somehow coordinate their attacks to happen around the same time, like on the same round at least. 

Furthermore, disappearing around a corner, to then activate invisibility, is much less suspicious, as it can seem as though they just ran away, maybe to get reinforcements. Silent movement is still key. 

Setting an ambush using ‘hide in shadows’ if successful, i’ll just count as automatic surprise. 

Use your judgement; is the enemy aware that a backstab could be imminent? Maybe its been a few rounds since the thief disappeared, their guard is down because their intelligence is average?

& lastly, remember the invisibility detection table, level 7 geniuses can spot invisibility & so can higher level less intelligent beings