How to still believe in the goodness of others after major disappointments?

Don’t. 
There’s nothing you could do about the behaviors of others. 
Focus on what you can control, as cliched as it may sound. Focus on your behaviors, be the goodness, the silver lining in people’s shadowed lives.

When someone treats you less than you deserve to, see how their behavior is just a proof of how badly they are managing their weakness and hurt. Don’t take it personally and feel sorry for them, not in a mean and mocking way. see how despite your scars and disappointments you have grown and healed enough to never treat anyone that way and feel grateful for that.

It’s very tempting to build walls around you after having been disappointed many times in a row in many ugly ways. But think of all the things you could be missing, all the friendships that could help you heal and grow, all the things you could learn from other people, all the value you could add and inspiration you could represent to hopeless and more scarred people.

Furthermore, by hiding your heart away in a shell, you risk turning it into a cold pebble that will soon loose its ability to feel and be alive with the warmth of human emotions and interactions.

Isn’t it sad to waste that in expense of fear of something you can’t control?!

be the goodness without expecting anything back, do good for yourself, for your God and trust Him and ask Him to keep away those who won’t add positive value to your life.

Be kind and have courage. Believe in the power of forgiveness and be the founder of goodness in hopeless places.