This is probably because of the widespread fear of mutants that caused the government to go over the top with the Sentinel program. Remeber that the Brotherhood and the X-Men pre-dated the Ultimates, and during that time, there was no well-known superhuman personalities that would be promoted as heroes to the public, just rogue vigilantes like Spider-Man and the X-Men.
Fear and paranoia caused by the destructive abilities of many mutant terrorist probably forced the government and many people to support "the greater good", such as trading the life of a mutant child who could possibly gain powers that would caused further violence and death across America. You could refer the "J", the poor kid in New Mutants who wiped out almost an entire town because of his mutant abilities, forcing Fury to have Wolverine put the poor kid down. We could also refer to teenage super-mutant Proteus who wreaked havoc across Europe by his sheer will. The government probably did not want to risk more mutants manifesting such dangerous super powers and declared an all-out war against mutantkind.
If it was not for the more high profile cases of the X-Men actions such as the rescue of the President's daughter, which garnered a lot of sympathy and eventual support from others, the Sentinel program would have been still accepted by the majority.
