Good luck BewareTheUndertoad - excellent name btw 
Thankfully our local dog-owners all seem to be good at picking up after their dogs & then disposing of the mess appropriately. So not in someone else's bin (unless they have permission, I guess) but in the dog poo bins in the local parks or the litterbins dotted about the streets. Or sometimes taking it home to their own bins, yes.
I live in an end-of-terrace house so my bins (brown for garden waste; green for recycling [only the lid in my case after it had to be replaced & the council had no green bins... but had green lids...?]; & black for everything else) are kept in the side passage. Due to my disability I'm on the "assisted collection" list, so (apart from the times they don't empty the bins at all & the times they empty them but don't return them 🙄) my bins aren't ever left within reach of the street.
Between the two things the bin-botherers have to open the gate & walk right down the passage to get to the bins; it's not a simple reaching into the garden/over the wall, or "ooh, the bins haven't been taken back in yet today". These are people who think it's fine to use our bins rather than wait until they get to one of the many public litter-bins within a few hundred metres - or even take their rubbish home with them, should their home be closer than the next bin. If you live in this borough you know all rubbish is meant to be bagged. And if you can cope with holding your fast-food box as you walk along consuming the contents, you can keep on carrying it once it's empty rather than dumping it into my bin.
I caused myself multiple joint dislocations & basically turned my knees into giant haematomas extracting wine bottles that had been deposited into my dustbin - with some of their contents still in them, so I then had to clean the bin. (I got a bit ambitious about my physical abilities/frustratedly dismissive of my limitations. And was worried about the bottles smashing & shards being left in the bin. Nobody about to help me, so...) The time I opened the bin to discover the remains of someone's picnic in a poorly-tied carrier bag was particularly stomach-churning - I'm almost!vegan & the sight & smell of the chicken drumsticks was... 🤢 managed to re-bag it without touching it - particularly frustrating = fact that, unless they had, for some reason, been having a full-on picnic in their car, it meant they'd not bothered to find a bin in the park for their rubbish & decided to use my bin when they got back to their car 
Was also massively unimpressed with the great eejit who tore open not one but TWO bin-bags of leaking tube-feed (one of the things of feed was damaged during transit & seemingly soya+fibre feed smells so delicious my cats chewed through the cardboard boxes & chomped through/into the tetra packs to try to get to it so I had to chuck a load of them [& clean a massive puddle of tube-feed out of the hall carpet]) to shove some rubbish in. If the letters they dumped hadn't been turned to mulch I'd have been tempted to go & fill their bin with the feed left in the pack after I'd only done a night feed at low volume. That stuff curdles in the heat. I actually had to put an extra dose of anti-emetic down my tube just to deal with cleaning the bin out. And needed a LOT of extra oxycodone to deal with the pain, too. Obviously I realise that most people wouldn't face an exacerbation of health problems/issues relating to their disabilit[y/ies] because of having to deal with what happens when other people go using their bins, but there are plenty of other problems it could cause people.
It would take ages to get the dustbin filled even when my DB's living here too (he splits his time between two cities for work) as we recycle/compost (as applicable) everything possible, but for lots of people, randomers chucking stuff in their bin can mean they can't fit their own rubbish or that it's overflowing & won't be emptied. With dog poo, you could be facing a rancid smell everytime you use your outside bin for a fortnight. And if a bag wasn't tied properly, or it tears, you may we'll be left scrubbing dog poo out of your bin. If stuff goes in the wrong bin you could cause contamination issues. In my borough a bag of dog poo casually chucked onto the top of my recycling would see my bin tagged as contaminated, not emptied, & if it happens multiple times I'd be fined.
I get the temptation to use someone else's bin when it would be convenient - but I keep hold of my rubbish until I find a bin, be that a litterbin in a public place, or my bin at home. It's pretty entitled (not a word I fling about with abandon, so we're clear) to make free with other people's stuff. Including their bins, which they pay for, to put their rubbish in, and have a right not to have filled with other people's (literal &/or metaphorical) crap. Gah.