Lightly defrost chicken in microwave to separate them I had two pieces of chicken breast in a tupperware container in my freezer. I wanted to separate them and put one in the fridge below, so I put it in the microwave on defrost (fairly weak machine, and defrost was the second lowest setting) for about 30s.

When it came out, the thinnest edges of the chicken became bendable, but still stiff. The other parts of the pieces were still stuck together, cold, and rigid.

I separated the two pieces by hand (it actually took a bit of force to bend them, and rip them apart because the thin transparent skin layer and the fat bound the pieces together when freezing), I then put one piece back in the same container, back into the freezer, and the other piece in another container into the fridge below.

I just bought them today, and the best before date is not for another 5 days. Before freezing, I rinsed them under very cold water, and patted them down with some Bounty towels.

I've been told to never refreeze meat after defrosting in the microwave. Is this still safe to eat or am I just being paranoid?
What you have done is fine. Not only are you not facing a safety issue, but because you didn't allow the piece that was to be refrozen to completely thaw, you're unlikely to even face the quality issues that refreezing poultry often sees. (Refreezing poultry tends to play a bit of havoc with the texture)

One small thing...our grandmothers rinsed chicken. It has been definitively shown that rinsing chicken (purchased from a reputable store) is unnecessary, and may actually do more harm than good because it doesn't significantly reduce pathogens on the surface of the chicken, but it will spread those pathogens (if present) around your kitchen.

Related: Cooking, freezing, recooking, and refreezing chicken