No. OK it depends.
The thing that people miss is that there is one unique factor that nobody else has and that is you. You are the thing that people are interested in, not your product or your services.
Most people, don't need to separate the work from the personal accounts. The reason why people say this is they expect to post corporate marketing on the work one. First and foremost nobody is interested in corporate marketing and what your company does.
And in fact, yes they are interested in you. Your social media profiles should be a reflection of you and your personality and not something you think they should represent.
Do I mix work and personal life, of course I do it makes the social media feeds more rounded and more human.
The one area that you might think about is if you work feel they own your social media feeds. Some do, they don't. Better than having an argument, you might want to plan for that situation. I created a work account just in case, so I would have given that back rather than my main twitter account.
There should be a balance between personal and professional lives on the web. While the balance differs from one person to another, many failed to address the limitations. If an employer disagrees on your social media profile, then the company may not be the best fit for you. The reason is simple: working at a place where you can't express who you are, won't be a pleasing experience. But this applies if your post in within the limit. For example, if you want work your career up at a company, but your last year's posts have shown that you hated its products, this can damage your career.