What does 才 mean in 什么样的人才能做以下职业?
I would not agree that this 才 is 'only', I'd plump for 'then', or better still ignore it in translation. And this use of 'then' really means 'in that case'.

什么样的人才能做以下职业？
What kind of person then can do the following job/jobs?

怎样才能算出我的税金？
How (then) can I figure out my taxes?

努力工作才能取得成功。
(If you) Work hard, then you will be successful.

夜里才能赞美今天晴朗的天气。
(Wait till) evening, then you can praise today's fair weather.
Praise a fair day at night.