Am I allowed to buy skills/tallents from tables of alternative ranks if I don't meet the prerequisites other than "You must be <Career>"?

I don't see a clear answer to your question, although I'm not overly familiar with the system. The top down method asks you to note any alternate ranks you wish to use before purchasing characteristic advances, so I would imagine you might need to meet characteristic prerequisites. What other prerequisites are there? If it's something you couldn't possibly meet during character creation no matter how much XP you had to spend or what choices you make, I think you might have a case for ignoring that prerequisite.

I had a fight with the GM cause we kept confusing skill/talent table prerequisites and rank prerequisites.
After literally 6th time I asked the question I finally got the answer that I MUST meet the rank prerequisites of Stats/Talents/Skills/Homeworld, but not the ones involving In-Game or backstory achievements.