Yes and no.
While there are no general laws that ban the display of offensive symbols, they are prohibited in certain circumstances. Significantly, this is in the workplace.
It is illegal to discriminate on the following bases in the workplace:
- National origin
- Disability (physical or mental, including HIV status)
- Age (for workers over 40)
- Military service or affiliation
- Bankruptcy or bad debts
- Genetic information
- Citizenship status (for citizens, permanent residents, temporary residents, refugees, and asylees)
For instance, in Burlington Industries, Inc. v. Ellerth, 524 US 742 (1998), the majority found:
a plaintiff claiming employment discrimination based upon race could assert a claim for a racially hostile work environment, in addition to the classic claim of so-called "disparate treatment."
Since you haven't been specific about the nature of the offensive symbol, some examples might be:
- displaying a swastika
- displaying sexually offensive material
- displaying racially offensive material
These are likely only to apply if the employer ought to have known, or did in fact know, that an employee (or in some cases, the customers) of a business would be offended, or it would amount to discrimination.
Of course, a single display of only the symbol is not likely, on its own, to create a hostile work environment - it would need to be considered with the rest of the facts - but it can certainly be a contributing factor.
It's a bit difficult to list all the situations where similar laws might apply, but this is one of the most prominent (and, to be honest, one of the ones that I'm personally interested in).