In his inaugural address, Wallace holds the opinion that Alabama should continue to be segregated.
This is evident from the first part of the quote in which he proclaims that he is in favor of "segregation today...segregation tomorrow...segregation forever." At this time, the US federal government was enforcing the ruling of different Supreme Court cases that ruled segregation in public facilities was illegal. This includes the famous Brown vs. Board of Education case. Governor Wallace is going to try to stop this integration at the University of Alabama, as he feels the federal government it's abusing its power by forcing integration in public universities.