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I read this book two years ago at a local library and can't remember the name of it. The book is really old, written in the 60s. It has a peach cover with multicolored text.

It's about a man living in a society on an alien planet where a prison ship had crashed and the survivors banded together to form a society. He gets a promotion to a telegraph operator. I think they called it semaphore operator.

There are giant squid predators that are in a relationship with the human population. They let them live in exchange for food and are worshipped by a theocracy. There is one particular big squid who is the King and he wrecks everything the protagonist had including killing his mentor after the protagonist started talking about how they were not beholden to the monsters.

Although I can't find the cover you mention, I think this is the Jack Vance novel The Blue World, first published in 1966. The Wikipedia plot summary matches the features you give:

Sklar Hast, the protagonist, had achieved a measure of success and prosperity by passing his examination to be a “Hoodwink”, or semaphore tower operator – a prestigious position on the Blue World, a planet with no land at all. During the space of twelve generations, the descendants of a crashed prison ship have created a rudimentary civilization on the water-covered planet, living on huge sea plants. ...

The world is mostly safe. However, they must beware the kragen, giant, semi-intelligent squid-like predators which roam the ocean. The colonists eventually develop a relationship with one of these, King Kragen. It drives off other kragen in return for offerings of food organized by an entrenched quasi-religious priesthood built up over generations. ...

When Sklar questions the need to continue to worship and feed this predator, King Kragen appears, wrecks his home and kills his mentor. Rather than regard this as divine punishment, Sklar suspects that the conservative priesthood has enough control over King Kragen to kill those who oppose their views, and to thus uphold their privileged status.