If everyone is on/of the Web, then you need to know how to be on/of the Web, no matter what your business is up to.
That doesn’t just mean figuring out a website.
It means leveraging the communication tools and methods unique to the Internet; reconsidering what an obtainable, understandable and malleable dataset is; and understanding how these tools and concepts may modify or even destroy your mission.
Do you hire external firms to do this on your behalf? Or hire your own? That’s a question of culture. But you need someone who cares about your mission and knows the tech.