Are you allowed to fraternize with customers, or clients outside of work?

That depends upon the business.

We're not allowed to date co workers at my work place. I don't have to deal with clients or customers.
We can socialize with co workers out side of work if we want to.

Employers can set rules about this which must be followed by their staff, with termination being the repercussion.

Its a good idea to be social with your customers, it solidifies the relationship. However, the definition of the term fraternize implies that the people shouldn't be entering into a relationship...since an issue on the personal side could affect business.

Pure company policy. Legally they can't stop you, but if it causes business issues they can let you go.

Why does what I'm allowed to do matter? If you meant to ask if you are allowed, that would depend upon the rules at your job. Prison guards, no. Sales people, of course.

That would depend upon your employer.

Yes, I mingle with them all the time.

Yeah.