Are friends, work, independence, recreation, and family support equally important for people with mental illness and people with other chronic illnesses?

No.

Explanation:

It depends on the mental illness if someone always wants to be alone they can have autophobia which if left untreated it can cause serious communication issues the person can have panic attacks if around little to a lot of people and sometimes even worse symptoms. But about chronic illness is basically the same as a mental illness however it is long term such as eating disorders which could be because the person uses food to suppress their emotions or it helps them cope with hard times.