How important is it to keep Kosher?
Firstly, every Mitzvah Hashem has given us is important, because it is important to him that we keep them. If a king would ask you for a simple thing like a to bring him a cup of water, surely you would immediately obey happily.
In addition, every Mitzvah has it’s details and ‘specialty’. As the saying goes, ‘you are what you eat’. Food a person eats later becomes a person’s own flesh and blood, and it is therefore very important to keep to the diet that Hashem prescribed for us, a diet that will make sure our flesh and blood are refined and holy. A person’s diet has an affect on his character, like the Ramban writes, that through eating meat of an animal who rips and eats other animals, the person grows an attribute of cruelty in him.
The Rebbe blames the current sad and low state of many Jews in a large part to a lack of keeping to the Kosher laws (in addition to the laws of family purity). Kashrus helps a person’s mind be clear and fine, and gives a person the power to overcome his bodily coarseness.
When people write to the Rebbe regarding health and digestive issues, the Rebbe often replies that such physical health issues come from the food that was not on a proper Kashrus level. This is similar to when one eats something physically rotten that might make him experience stomach problems. So too when he eats something spiritually rotten.