"Strong opposition" means having a powerful disagreement or resistance towards something or someone. It implies taking a firm and determined stance against someone or something. Full definition
The state's plans face strong opposition from cat lovers who feed and care for colonies of feral cats. (articles.orlandosentinel.com)
The close vote was not, however, a clear victory for lawmakers who are expected to face strong opposition in the coming weeks and months until the ban takes effect. (dogingtonpost.com)
The bill faces strong opposition from breeders that claim it will put their puppy mills out of business. (animallawcoalition.com)