What Diseases Are Linked to Microbiome Imbalance?
If a healthy microbiome exists, then an unhealthy one must as well. Skin diseases almost always have a genetic basis, but external factors significantly influence their manifestation. The human microbiome is being studied so thoroughly by so many people and institutions that new research emerges practically every month—it's hard to keep up. Skin diseases are typically linked to weakened skin immunity and a compromised barrier.
The microbiome significantly impacts both of these indicators. Currently, the three main diseases where the microbiome is considered are acne, atopic dermatitis, and psoriasis. Less frequently, the microbiome is mentioned in the context of seborrheic dermatitis and dandruff.

How to Maintain a Healthy Microbiome and Avoid Harming It
Don't wash with harsh products; if possible, cleanse and wash your face with water only. Don't use too much cosmetic product, and avoid constantly using products with high alcohol content. Don't exfoliate your skin excessively. Don't try to fight with your skin; instead, befriend it and allow it to cope with everything on its own. Don't over-treat it; instead, help it. In short, embrace the "less is more" rule and live by it calmly.
Of course, we're not suggesting you give up cosmetics entirely (though a two-week quest like that would be beneficial for anyone). I propose not overdoing it with cosmetics and using exactly as much as needed. For this, however, you need to thoroughly understand which product you're using and for what purpose. In other words, don't use cosmetics designed to solve problems you don't have.
Regarding food, it's also quite straightforward: eat a more varied diet, consume more fresh vegetables, and try to gradually reduce the amount of highly processed foods. This is good not only for the microbiome but for overall health.