Assuming I have a profession A, and I'm trained in a very different one as well, B.
Shall I mix both in my profile, or will it just create an impression of being all over the place?
(I'm currently looking for work in A, and B is from a completely irrelevant realm to A).
The purpose of the LinkedIn is so current and former coworkers can find you, and so recruiters and hiring managers can find you.
Why would you not include all work experience? You might have a degree in Biology and worked for the first 5 years in a laboratory, now you are an accountant. A company working in biology, pharmacology, and chem-bio defense would be very interested in you. Because you are accountant with familiarity with the subject matter.
Former co-workers who could expand your network would not be sure it was you if you didn't include all the places you worked, thus potentially missing out on a source of job references.
Also splitting you experience into two profiles will show that both halves of you have trouble staying employed because of all the gaps in experience.
(to paraphrase a little...)
I'm currently looking for work in Field A. I also have experience in Field B, but is completely irrelevant to Field A. Should I include both experiences on my LinkedIn account?
It doesn't matter. Showing just your experience in Field A would make for clear, succinct profile for a hiring manager looking for just that skills, specifically. But, people change jobs/careers so often these days that it's standard for your LinkedIn profile to be more of a CV than a resume: i.e. it's for listing everything you've done, professionally, and not just your qualifications for one specific position. Hiring managers shouldn't see anything odd in a LinkedIn profile that lists all your professional activity. At the very least, your experience in Field B could help you show generic leadership / communication skills, and fill any apparent time gaps (for hiring managers that still look for those).
Note, however, that for the related question...
I'm looking for a job. I have experience in a couple different areas, and I'd love to work in any of them again. Should I put everything on my LinkedIn profile?
The answer is (a definite): Yes! Again, your LinkedIn profile is more of a CV than a resume. You want to draw interest from all those fields, so list everything.
Cross specialization is useful to a very small subset of people. If you're doing a lot of IT but you also have background in Geology there are people that can use the combined experience. If you can provide more details it's easier to figure out the specifics.
