For State statistics on Age, Gender, Race, Education, Income, Poverty Levels, Disability, Ethnicity (Ancestry), Marital Status and Veteran numbers:
U.S. Census - Type in the name of the state in the search box to find Age, Gender and Race, Demographic and Housing Estimates (Age, Sex, Race, Households and Housing, ...) data for your state. For more information, look at the Related Searches info to the right of your search.
For State statistics on Religion:
Pew Research - Religious Landscape Study (scroll down to Geography and select the state you want).