Do I really need to use TSP when restaining my kitchen cabinets?

No...You can clean the cabinets with other cleaners.

I have read where you can use a good degreaser, but I'm not sure why you won't want to use TSP. It's a very safe product that is biodegradable with no VOC's. It also helps control any lead dust if you home is older and has lead paint underneath the surface. I'm guessing if your cabinets have been stained, lead paint is not an issue but you never know. I have copied the product overview from Home Depot. I'll put the link at the end.

Use TSP Heavy-Duty Cleaner to clean and prepare your Home, Decks and Siding for painting. The cleaner removes Dirt,Grease,Grime,Soot and Chalked Paint. It is compatible with washable walls, floors and woodwork including decks and siding. It is specially formulated to control lead paint dust.

• Removes deposits of grease, grime, smoke, soot, stains and chalked paint
• Suitable with most washable walls, floors and woodwork including decks and siding
• Powder mix design
• Cleans surfaces in preparation for painting
• Non-corrosive
• Biodegradable
• ZERO-VOC formula

It is specially formulated to control lead paint dust

Copied from: http://www.homedepot.com/p/SAVOGRAN-1-lb-Box-TSP-Heavy-Duty-Cleaner-10621/202935861

You need to thoroughly degrease them, or the stain won't stick. You can scrub them with Dawn, rinse, and scrub again -- but wiping them down with TSP will save you a lot of elbow grease.

Better be safe then sorry...You want the cleanest surface possible, without any grease.

you have to degrease them. I'm not sure the TSP out now is like the original, so blue Dawn is the best degreaser around. Sort if wash, rinse and dry.

TSP is cheap and worth the labor for a terrific paint job