Objection 1. It would seem that confession of faith is not necessary for salvation. For, seemingly, a thing is sufficient for salvation, if it is a means of attaining the end of virtue. Now the proper end of faith is the union of the human mind with Divine truth, and this can be realized without any outward confession. Therefore confession of faith is not necessary for salvation.
Objection 2. Further, by outward confession of faith, a man reveals his faith to another man. But this is unnecessary save for those who have to instruct others in the faith. Therefore it seems that the simple folk are not bound to confess the faith.
Objection 3. Further, whatever may tend to scandalize and disturb others, is not necessary for salvation, for the Apostle says (1 Corinthians 10:32): "Be without offense to the Jews and to the gentiles and to the Church of God." Now confession of faith sometimes causes a disturbance among unbelievers. Therefore it is not necessary for salvation.
On the contrary, The Apostle says (Romans 10:10): "With the heart we believe unto justice; but with the mouth, confession is made unto salvation."
I answer that, Things that are necessary for salvation come under the precepts of the Divine law. Now since confession of faith is something affirmative, it can only fall under an affirmative precept. Hence its necessity for salvation depends on how it falls under an affirmative precept of the Divine law. Now affirmative precepts as stated above (I-II, 71, 5, ad 3; I-II, 88, 1, ad 2) do not bind for always, although they are always binding; but they bind as to place and time according to other due circumstances, in respect of which human acts have to be regulated in order to be acts of virtue.
Thus then it is not necessary for salvation to confess one's faith at all times and in all places, but in certain places and at certain times, when, namely, by omitting to do so, we would deprive God of due honor, or our neighbor of a service that we ought to render him: for instance, if a man, on being asked about his faith, were to remain silent, so as to make people believe either that he is without faith, or that the faith is false, or so as to turn others away from the faith; for in such cases as these, confession of faith is necessary for salvation.
Reply to Objection 1. The end of faith, even as of the other virtues, must be referred to the end of charity, which is the love of God and our neighbor. Consequently when God's honor and our neighbor's good demand, man should not be contented with being united by faith to God's truth, but ought to confess his faith outwardly.
Reply to Objection 2. In cases of necessity where faith is in danger, every one is bound to proclaim his faith to others, either to give good example and encouragement to the rest of the faithful, or to check the attacks of unbelievers: but at other times it is not the duty of all the faithful to instruct others in the faith.
Reply to Objection 3. There is nothing commendable in making a public confession of one's faith, if it causes a disturbance among unbelievers, without any profit either to the faith or to the faithful. Hence Our Lord said (Matthew 7:6): "Give not that which is holy to dogs, neither cast ye your pearls before swine... lest turning upon you, they tear you." Yet, if there is hope of profit to the faith, or if there be urgency, a man should disregard the disturbance of unbelievers, and confess his faith in public. Hence it is written (Matthew 15:12) that when the disciples had said to Our Lord that "the Pharisee, when they heard this word, were scandalized," He answered: "Let them alone, they are blind, and leaders of the blind."
Source: Summa Theologica (New Advent)