Wiring – the new exhaust bathroom fan wiring issue

Don't overcomplicate it. Sounds like you had a "fan and light" with wiring to be able to be switched separately, but actually wired so they were always switched together.

So, remove and insulate the red (what you call pink, but it's both commonly and clearly in your pictures: red) wire at both ends. Twisting on a small wirenut and taping that is a typical approach. You don't need it unless you want to have separately switched fan and light on a fixture that supports that, perhaps the next remodel.

Black to black, white to white, bare to green, call it a day.

Yes, you COULD leave the red and black together, but it's not actually right to do that if they are going to the same wire - fine when you had two separate wires at the fan, not fine without that.

Yes, they are giving you separate neutrals so you have the flexibility to put the fan and light on different circuits if you want to. Neutrals must be supplied from the same circuit as the hot; you can't return current from circuit 1 on the neutral from circuit 2, or it causes a number of problems and safety threats.

In an application like yours, feel free to tie the neutrals together using your preferred wiring method.

Once that and the grounds are hooked up, you have 2 from the ceiling and 2 left on the fan. One wire is for the fan, the other for the light. Generally blue is for the light. I have no idea if your house was wired black for the light or red for the light, but whatever. Hook it up one way e.g. black-black blue-red, and if that doesn't do what you want, then hook it up the other way e.g. black-red blue-black.

Make sure not to put a fan on a dimmer by mistake!