Is abstaining from a door of good that would cause strife in the religion the correct action according to Sharia, and is one rewarded for the good he intended to do through it, and will Allah compensate him with other doors of good?

The questioner did not specify the nature of this "door of good" nor the corrupting consequences resulting from it. However, if engaging in this "door of good" leads to committing a sin, then the principle is to prioritize warding off harm over achieving benefit. It is not permissible to commit a sin for the sake of performing a non-obligatory good deed. If Allah knows the sincerity of a person's intention to do good, and that they are prevented by fear of committing a sin, then He will reward them for their intention. And they should strive in supplicating to Allah to facilitate a "door of good" that contains no prohibitions.