But realize that the customer not only heard your profanity, but also whatever you were "venting" about -- if it was employment related (supervisor, coworker, other customers, product, etc) and this is a customer service/front facing position, that will probably be taken into account. And you were in a place to be overheard and didn't notice/care.bb As will your less than 90 days of service. Unfortunately that is not a lot of time to build up any goodwill/work habits/performance for them to realize this is a "one-off" to your real personality/job performance. If anything, most employees do their very best in the beginning and then tend to get more comfortable over time.
There is a common law doctrine called "duty of loyalty" -- The laws in every state require that an employee refrain from behaving in a manner that would be contrary to his employer's interests...your employer isn't required to tolerate employee behavior that's contrary to its interests. You have a responsibility to your company that doesn't end when they clock out. -- from hrhero.com
I honestly would advise one of my managers to let you go...why? Because when people/employees show you who they are, believe them. Honestly, lots of employment issues could be solved if managers would follow this principle.
Lesson learned....don't vent/use profanity in your workplace even when you are not on the clock unless it is a protect concerted activity between employees who are working for better wages, working conditions, etc.