Do I really need to wear a white robe for planetary magick?
A caveat is only if the particular system of planetary magick you are working in requires it.
It’s like candle colour. It only matters within the system you are using. Otherwise, you could wear purple with yellow polka dots with no issues.
Both my books mention one but idk. I only have a black robe and it was kinda expensive
Adapt. Wear a white t-shirt instead then.
I assume the books give some significance to the colour and so it is deemed necessary.
Well, the magick comes from you, not from your robes. You can do magick naked so whatever you wear is not that important, unless you FEEL it is. If you feel it is important, if you believe it is, then yes, it will be important for the success of your craft. Up to you. Up to your beliefs.
Theoretically you may wear white clothes in order to either do a Moon working (spell, evocation…) or to operate White Magick: that is, positive according to the modern/scientific High Magick paradigm; generic and neutral (in a way, every type of operation) according to orthodox High Magick.
But yes, like with circle and even sigils, it’s not strictly required.
A white robe?
I typically wear a gray t-shirt and a pair of blue jeans, but the spirits are lucky if I even bother to wear pants.
Color can trigger a psychological response but I find that it varies by person (for example, one person may associate red with violence while another might finding it extremely warm and comforting). I would recommend exploring what psychological response the authors are expecting the reader to have while wearing it and picking a color of clothes that triggers that with you
Edit: if they are talking about a hooded robe in particular, one of the effects they are hinting out is the “distant” sensation that comes from part of your vision being blocked. That can be substituted with a much more affordable hoody or a medieval style cloak which is essentially a blanket latched with a brooch that you can pull part of up to make a “hood”