Glossary and preface:
- MSA = Microsoft Account, formerly known as Microsoft Passport, Microsoft Live ID, etc.
- OA = Organizational Account, e.g. an Office 365 "employee" account.
- An OA is not necessarily an MSA and different OAs and MSAs can even share the same sign-in e-mail address.
- Microsoft is doing something about this mess, but it's still a mess.
On to your problem:
Visual Studio lets you use multiple accounts (MSA and OAs) for accessing resources (Azure, etc) and for licensing, but it only uses a single account (which must be an MSA, not an OA) for personalization. This is by design.
Here's a screenshot of my Visual Studio 2017 Account settings page. (Note: I activated my install using a Product Key instead of using an account):

You said you have two accounts: a work account and a personal account. Presumably these are both MSAs as you say you're also able to use it for personalization. I think you should avoid using your work account as the Personalization Account entirely and only use your personal MSA for that (assuming you want those single settings to be applied to both your home and work VS installs). You would still have your work account listed in the "All accounts" list, of course.
One of the ideas behind having single MSAs that are associated only with you and not your employer or other company is that employers and orgs would use Azure AD to let you authenticate with your personal MSA to access company resources. This didn't turn-out well in practice and it doesn't seem right that companies would add delegated authentication using peoples' personal (and often unprofessional) email addresses (imagine logging-in to your work desktop computer using x360xnoscopexlol@gmail.com
while wearing a suit and tie).
You can still use a personal MSA to personalize Visual Studio, as if any of the OA accounts are associated with a Visual Studio purchase or MSDN subscription then VS will consider itself licensed.
All that aside, you have several options:
- Don't use any Personalization Account and keep your settings in-sync by manually using the Tools > Import/Export Settings feature. This gives you the most control and lets you have per-machine settings.
- Use a single personal MSA for all VS installs. This is the scenario I described in the previous paragraphs. It's what I use and recommend. You'll only run into issues if you have an unenlightened IT department or boss that forbids the use of "personal" accounts for anything company-related.
- Use multiple personalization accounts and manually switch between them. (This is the "grin-and-bear-it" option. You could use a password manager and program like Autohotkeys to automate the process of switching between accounts though).