In Luke 10:25-37 (the parable of the Good Samaritan), Jesus says that if you love your neighbor as yourself, you will be saved. In this self-contained passage, Jesus does not mention faith or belief, in the trinity or otherwise. The example he uses of that love of neighbor is of the non-believing enemy, the Samaritan.
In Matthew 25:31-46, Jesus describes the final judgment and says that if you show compassionate for those who are hungry, thirsty, naked, sick, in prison, strangers or all those he called “the least of these,” you will be saved. Period. Again, no mention of faith or belief, in the trinity or otherwise.
I take him at his word on this.