What does "You can't bolt your door with a boiled carrot" mean?
Solution 1:
The answer can be found (surprisingly) on Foxtowe Shaker Doors (a British door maker's web site): https://www.shakerdoors.co.uk/never-bolt-your-door-with-a-boiled-carrot/
Of course, it is highly unlikely that anyone would actually try to bolt their door with a boiled carrot, rather, the implied meaning behind this proverb is that you should act carefully, and plan ahead for any potential future problems. If you were to bolt your door with a boiled carrot, anyone, friend or foe, would be able to enter your home with ease, whereas if you had a proper lock and bolt on your door, you would be quite safe.
From this I would take the meaning as "Do the job properly and thoroughly: do not take shortcuts."
Solution 2:
Why look further than the plain sense that can be read into that and suspect that the irish have a special way to conceive this image? Obviously, the carrot is the bolt that you slide (partly) from a ring structure (or tubular structure) fixed to the door frame into another such structure, that one fixed to the door, thus locking the door to the frame. If that bolt is replaced by a boiled carrot, well, the smallest pressure on the door will tear the carrot apart.