There was an opposition. The reasons were mainly philosophical. The main thing which was hard to accept was "action at a distance" through the void space. For example Huygens did not accept this. It contradicted Descartes theory which was prevalent at that time. So the question had too be decided by observations and experiments, as it always happens in science.
And it was decided in the most spectacular way. The crucial successes were: prediction of the correct shape of the Earth, explanation of inequalities of Moon motion which led to very exact predictions of the Moon position in the sky. And the final great success: the discovery of new planets, big (Neptune) and small (asteroids).
After the discovery of Neptune, NO SERIOUS SCIENTIST could have any doubt in the correctness of the theory.
Here I am in a strong disagreement with Conifold. Newton's mechanics is correct. Because it explains and predicts observations and experiments correctly, and with very high accuracy. It is the cornerstone of the whole physics, and one of the most successful scientific theories. It is taught nowadays at all level from elementary school to the universities, and it is still an important research topic. And will probably always be.
And general relativity or quantum mechanics did not diminish its value. It is ridiculous to say that "it was replaced"!