We ate out a lot because it was summer when DS turned 6 months so I often threw a picnic in a bag to whizz us out between sleeps. Also ate in cafes and restaurants too. Actually I think his first piece of solid was in a pub for lunch, I had not planned for him to eat but that's how it turned out - a case of hand him some food or I'd have to leave because he'd scream the place down. In my head I'd imagined some perfect planning on solids introduction, just didn't turn out like that.
For picnic out door eating I took a picnic blanket, some food, water, a wet face cloth in a zip-lock bag for his hands and face and a small pack of hand wipes for emergencies, usually a muslin for a bib. He didn't really drop his food but if he did it would be onto a muslin I suppose so I'd consider it clean enough to be picked up again.
I always travelled very light so if it was just taking food for him (ie not a full picnic for me too) it would be literally be a couple of tubs thrown into my hand bag and a wet cloth.
We went out for Sunday roast when he was only just 6 months, I steamed some veggies to take so I had something similar to our meal but prepared salt free and in finger sized batons. He was given a few bits from our plates too (hunk of beef off my mum with a dab of gravy on it, that would have been salty but just a tiny amount) a roast potato, bit of yorkshire pud etc. Steaming the veggies for him only took about 10 mins and just put them in a small tub, probably another tub of fruit knowing me and maybe a tub of bread sticks or pancakes too (I always made sure he had something to eat whilst we waited for our order or he'd get impatient).
I sometimes asked in a cafe or restaurant for them to clean the high chair tray (some of them are gross) and sometimes used my emergency wipes to clean it down or wipe the table if the chair had no tray and if I had no plate. When he was a little older I carried a plastic plate, plastic sippy cup, kids fork in a zip lock bag and I did take a bib (the waterproof sort), and still put a muslin around his waist which covered his legs and clothes and also prevented some food dropping to the floor. Some places washed the fork and plate up for me and returned them to us, others didn't and I just popped them back into the bag dirty, no problem.
The only reason I took a fork to a restaurant is because he used a fork often at home, he started with it pretty early, to begin with a small plastic fork then a kids metal fork. He did find some adult forks quite heavy and hard to use properly. I later took the full set, knife, fork, spoon.
I really didn't find BLW all that messy tbh. I think the only time he ever ate in just a nappy was when we had a heat wave and he was not dressed anyway, I never stripped him for meals otherwise.
The ikea antiplop is certain the best high chair ever! We used it out on our roof terrace and in the kitchen at home (we have the baby dan at the dining table), it certainly provides an instant clean area to place food but then a plastic plate does that too if it's just a place for food you need. If you're home and going into the garden to sit on grass you could use a large tray (set of 3 from the £ shop comes to mind, yk just tea trays) to place in front of him, easy to carry and clean. I wouldn't bother taking anything 'special' out to cafe's though cos it just adds to the amount of stuff you've got to carry.
I have a vague memory of having a fold up plastic change mat (very thin though, not a comfy change mat, a thin cheap thing that folded up tiny) which could act like a waterproof picnic blanket for DS if I needed him to sit on someone's carpet to eat. I think it was something I just had in the car rather than something I carried all around.
