There were (and still exist) problems with pension fund contributions being recognized, but that's more on the pension fund to figure out (I've got 11 months of payments from 2011 that they are not registering because of this, which is why I switched to self-employment then).
But this is also ignoring the fact that all these years until early in 2020, Serbia had an extremely low-tax mode of operation for such workers: self-employment with taxation on a predetermined fixed "income" up to an actual yearly income of 6 million RSD (~50,000 EUR). For IT workers, who had the biggest tax rates in those arrangements, it was not more than 400€ a month, which is pretty amazing for up to 4500€ of gross income. This arrangement only required registration with the tax office and business registry that you are operating a self-employment agency.
Sure, those at the lower end or irregular income wouldn't benefit from it, but Serbian government is already mostly forgiving their debt for anyone with less than 500€ of monthly income, and spreading the debt over 10 years, which are the terms protesters are not accepting.
I also think it'd be acceptable to offer the same taxation rate to anyone who would have been eligible for self-employement fixed-tax if it is more beneficial, and the accumulated interest would be the only "penalty" for skipping taxes.
That way people who did pay taxes wouldn't feel disadvantaged over the ones who avoided them.