No, I do not think that if someone is a really good worker, and that they can help out a business a lot, if they say something that is the wrong thing they should not be fired. It should be based on how good they are at the job the do.
If it is a first-time offense, the manager or HR should just let is slide. If it is the third or fourth, maybe firing would be appropriate. Everyone makes mistakes, and everyone hits their end of the fuse and blows up. However, you have to learn from the first time and make it better.
Employees should not be fired for saying the wrong thing at work. Employees should be protected under the first amendment which permits the freedom of speech and expression. People should not be discriminated against if they have an opinion which differs from their employer's opinion. Punishing someone for their opinion is un-American and un-constitutional.
I believe employees can cross a line where it is plausible for them to be fired for saying the wrong thing at work. There is vile language and the workplace is not the place for that. However, I do not think you can lump all of these individual and probably different circumstances into the exact same group. It's best to remember that most American employment is at will, so your employer can fire you for no reason at all, if that's what they so wish to do.
No, I do not believe that employees should be fired for saying the "wrong thing" at work. What is the wrong thing exactly. We are supposed to have freedom of speech. If something is said that offends then an apology should be warranted, but being fired is far fetched. If people were fired every time they said something stupid or wrong we would all be out of work.