I think it depends on the field that you're in. In consulting, for example, your resume may be included in proposals and some clients look for things like awards, degrees, and memberships in professional organizations. So it's important to have those memberships even if your employer offers training and continuing education in your field, and membership in a professional organization would provide no actual benefits to you. It can be all about appearances, and sometimes appearances count more than substance.
I work in consulting and have let my membership in professional organizations lapse over the years, mainly because I wasn't getting anything out of them; it doesn't seem to have hurt my career. But I'm far enough along in my career that the big selling point to my clients is my experience and expertise, not my academic credentials or membership in organizations.
Maybe it's more important to join a professional organization when you're young, or when you're job hunting (professional organizations often provide networking and job-hunting opportunities), and becomes less important the more established you are in your career. Of course there are other reasons to join these organizations and some people find it personally enriching to contribute to the advancement of their field via a professional organization.