Do you believe in forgiving friends who betray your trust?

I may and frequently forgive people as human beings.
That doesn´t mean to keep them as friends, a "job" they had voluntarily quit from.

It depends...
Let me put it this way. A relationship between two people is like a glass.
Some glasses are stronger and meant to last more, like those you have with family or very close friends.
Others are thinner, for example an acquaintance or someone you just met..

If the other person does something minor, it looks like a stain on the glass. You wipe it away and forget it.

Other things might cause a little rupture in the glass. Maybe in a corner somewhere out of you direct sight. Occasionally your eye might wander of to it and you remember what caused it, but you are able to oversee it for most of the time.

But, small ruptures night add up and become more and more visible and annoying for you... so in that case, you might cut off with that person because looking through the glass is not pleasant anymore.

And finally there are some things that can shatter the glass. And because of its nature it can't be replaced or fixed. In those cases trust is gone, along with the relationship you had with the person.

Now it is up to you to decide what you can oversee and what not... But I know that when my glass is shattered there's no going back...

Examples of yes and no:
I forgave a friend for bailing on my wedding for what I deemed to be selfish reasons.
I will never forgive my childhood best friend for sleeping with the guy I was dating.

I find it very difficult once the trust has gone, I choose my friends wisely & keep them close

Nope. I overheard a supposed friend trying to turn my other friends against me. Permanent ban!

Yes, but I don't believe in placing myself in position to be harmed by them again.

not really...

would never trust them as much again.

Reading this brought tears to my eyes. What an absolutely beautiful person he is.
https://www.yahoo.com/gma/botham-jeans-brother-discusses-emotional-courtroom-hug-amber-113807976--abc-news-topstories.html

No...that would be like being bitten by a pet snake on Thursday, and then deciding to cuddle it on Friday.

I tend to become extremely hurt when betrayed. I don't give betrayers 2nd chances.

I can forgive but I can never forget.

Forgive, yes. Forget, never.

Depends on a few things: the circumstances of the betrayal, how close and long-standing the friendship.

I have to believe in forgiveness. But granting trust again is another matter, and in my case: no