Do sociology and classics majors get good jobs with high salaries?

Yes! it is possible, but I'd recommend getting hard skills as well.

I have a philosophy degree, but I have a great career in mortgage finance, due to additional career training and coding that I got on the job and going to grad school at night.

There are some opportunities, but most of them will be outside your core competencies that you build in school. Training in reading and critical analysis will prove useful in almost any field.

From a sociology perspective, understanding people and people systems may be relevant in the various fiefdoms and personality run business that are more common than one might think.

You should also network outside of your major and find friends with jobs you want .

Finally, a lot of jobs will require a degree but not strictly require that it is relevant. It will remain up to you to sell yourself and skills as relevant to the challenges of today. Also consider graduate programs that actually enhance your earning potential instead of a vanity degree.

I have a BA double major in Psychology and Sociology, however, I have worked in the Real Estate industry for most of my career. Many companies just like the fact that you have a degree in something but as far as making a high salary in the field of Psychology or Sociology its possible if you can get a job in the right company or if move up over time, but generally the starting pay in these fields will be low. A higher salary is more likely if you pursue a masters degree or doctorate.

Not necessarily in the same field as the major although it is possible if you continue with a graduate degree and go into academics. Those majors can be interesting to recruiting managers and allow you to provide a different perspective if you enter a field like business, tech, finance.

Recommend watching School of life videos. You may get some insight