I've been an academic, and now I'm working professionally. I can tell you what I've experienced. First, let me answer the question:
A "research foundation", in my opinion, would be academia. The foundation will usually pursue the same types of funding opportunities as a university, usually competing directly against them. Next, and the important part, working for one will ultimately NOT be a factor in whether you land some position in the private sector, however, there is a caveat to that.
For a given position, that organization will have its opinions on whether an academic is someone that should be hired. What I found, in moving from academia (university professor) to the private sector is that headhunting/recruiting firms will either not touch you, or be ineffective in presenting you to potential employers. Whatever position you land after leaving academia will be based on your own footwork, so be prepared to do a lot of weeding through job boards looking for actual employers and not recruiting firms.
Of the positions you find on your own, some company will decide that having a person in their organization that has academic experience, such as a research foundation, is more desirable than someone without. Are those companies hard to find? Yup. Do they exist? Yup. The company I'm working for now is rather small, but growing. Smaller companies are the types of positions you can expect when leaving academia and moving into private sector.
Another type of company that you can expect to hire you would be very large companies. If you're going to search a job board for one of these employers, you'll end up getting a bunch of recruiters, which you don't want because they won't present you properly, if at all. To get hired at an in-field, large company (BASF, 3M, or Dow Chemical, for examples in your field), you will need to go directly to their website and put in your application if you want to be considered.
Finally, as suggested by another responder, consider working for the government, or pseudo-government agencies (like the F.D.A., in the U.S.). This may be difficult to do if you're not a citizen of the country where you're applying, so read government postings carefully to determine if you have the citizenship requirements for the position. Even if this isn't ultimately what you want to do, the experience will be considered more valuable to a wider swath of private sector employers than academic experience, making you, ultimately, more "hire-able" when you apply for positions six to 12 months down the road.
All the positions I received interviews for when leaving academia were companies that were doing direct hires. I did not receive a single interview based on a recruiter presentation, including one recruiter that had the audacity to insult me because I was coming out of work as a university professor. Not all recruiting agencies are that evil, but I repeat, I didn't get a single interview based off a recruiter: they all came from organizations, mostly smaller, that wanted my particular skill set.
Good luck and Godspeed!