I think that our attachment styles have a lot to do with our therapy, but they can be changed as the result of a good relationship. And the spots in our attachment that are not so healthy can come up too so we get to work on them.
I have avoidant or disorganized attachment styles that are still present even though I now mainly have secure attachments. Under stress the older, formative attachment issues come out more strongly. Just being aware of this and trying to work with it with some understanding and compassion has helped a lot to veer more toward secure attachments.