It's a really good question. As people have pointed out, there are many answers here. I think it's important to think about "barriers" to becoming a therapist and to accessing therapy in very broad terms. For example, it would be unusual in most places for a counselling or clinical psychology program to overtly state that members of certain ethnic groups were discourged from applying. However, the cost of tuition, the language of instruction, the ethnic makeup of the faculty, the location of the school and which thinkers and philosophies are included in the curriculum will all have a huge impact on how accessible or attractive the specific program and often the entire discipline will be to various groups of potential applicants. The same barriers will apply to clients and potential clients.

I was briefly in therapy in my second language (which I speak quite fluently) with a T who knew little about my ethnic/cultural background (and wasn't so interested) and was ever so slightly homophobic. It was okay enough but I never fully opened up to her and while I trusted her with my meds (she was a pdoc who was great with meds!), I didn't really ever want to talk about my feelings. It was a time in my life when I desperately needed therapy and could not have afforded to pay out of pocket and pdocs are fully covered by the public plan. It was definitely better than nothing, but also nothing like the really good therapy I've since had.

I offer this little anecdote because it helped me--overall a quite privileged person--understand a bit about barriers. It is harder to open up in a language other than your first language. It is hard to open up if you think that your T regards your ethnic group, your sexuality or some other component of your identity as inferior or somehow inherently pathological. And it can be a self-perpetuating problem because the less diverse the group of trainees in counselling/psychotherapy programs, the less enlightened all T's will be about issues of diversity and the less likely clients from diverse groups will be to seek out therapy.