Yes. Hash table, linked list and a graph of some sort are those fundamental datastructures that everyone should have implemented at least once by themselves. IMO, the core to excellent software engineering his having a lucid intuition about fundamental things such as those.
Mainly because they are simple, and lot of problems are solvable by using them without resorting to Someone Elses Gigantic Platform Framework.
In my experience, there's strong correlation between programmers that don't know how to implement basic data structures and programmers that make poor decisions when picking up one from a collections library. The ones that know that they don't know at least stick to fixed sized arrays and pay the performance price.
So, no... and yes. You can call yourself a software engineer without knowing any of this stuff, but you will be a better one if you do.
Learning what it is and how it works is necessary. From there, any remotely competent programmer should be able to quickly and easily create one.
Programming isn't about learning how to create specific things. But learning how to create specific things can help you gain the intuition necessary to create other things.
In C.. Yes.. it's a basic data type you'll probably find yourself using quite a bit. If you program in some other language that already provides hashtable functions/types, then maybe you can get by with just knowing how it works so you can figure out when to use it.
Mainly because they are simple, and lot of problems are solvable by using them without resorting to Someone Elses Gigantic Platform Framework.