It's also important to remember that there are various forms of segregation and integration, some that refer to a person's identity and some that refer to a person's skillset.
Gender discrimination and segregation is still very common, and much more so than ethnic segregation in my opinion. Not sure exactly what you mean by "identify with", but I'll assume you mean to recognize or be aware of. If we look at the number of minority or female owned businesses in the US, or those who have CEOs who are women or minorities, that can be indicative. There is also general segregation - such as, does the custodial or clerical staff contain mostly women or minorities? What is the average salary of each group within a company.
There has been a concerted effort in the last two decades to include more minority and female hiring practices, in an attempt to comply with federal law, affirmative action programs and as it is also a sound business practice.
Lastly, segregation by skillset is typical, and practical. The accountants work in accounting, the engineers in engineering, etc. You will also find a company is pretty typically segregated into management and labor - they don't intermix much and there is often tension between them.
I think you are asking how you can tell if minority groups are being segregated by a company they work for or if they are actually being assimilated into the company just like anyone else.
Legally, this is very hard. It is very hard to prove discrimination in any particular case. The courts have ruled that you cannot say a company discriminates, for example, just because it has few minorities in management and many in lower positions.
If you are asking about this just from the point of view of the company trying to get the most out of its workers, I would think you might try to look at work teams and see if they are segregated. You might also try to analyze email patterns and see if minorities and majorities email each other way less than they email within their own groups.