What jobs in what sectors/industries do not mind you having a side income/investment?

The old adage is that if you get a second source of income alongside your current job, your employer might discriminate against you in terms of raises and promotions.
I get that with certain jobs having a side hustle/investments, you will have issues with the side job affecting your performance in the first job, the investment/job might introduce conflicts of interest, and the second job might introduce privacy or intellectual property concerns.

Aside from legitimate concerns, I have heard employers don't like side income sources because it means you're less reliant on the primary source of income (and hence less motivated/they have less control), and it shows less commitment to the organisation/concern over the job. It can reduce the chance of you getting the raise or promotions even though you deserve them (because you need them less).

In some circumstances, the financial situation cannot be helped e.g. you live in a ridiculously expensive city and your pay doesn't cover basic expenses but you're passionate about the job/career. Alternatively, you might have chosen to go into the career, but you have racked up ridiculous expenses from the extensive number of degrees (necessary for the job) and associated tuition fees in the process . As the financial return of a degree for a lot of jobs has plummeted, it cannot be expected you can solely rely on one income for some jobs to carry you through, especially if you have to also contend with owning a house, raising a family, gathering sufficient funds for retirement, etc.

So, what jobs/careers are people in where they have seen their employers not raising a concern over having second income sources?

I'm particularly concerned when it comes to research based roles/jobs, particularly if it's science based research. I'm also concerned where it involves engineering research as well, considering how some roles aren't well paid.
I might understand if the job was involved in some areas of finance, law, tech giants, a CEO based role, or well funded startup companies, but I have yet to see it elsewhere.
The sectors where I have not seen it being an issue include catering, healthcare, and education.