Fully-aquatic mammals that I can think of, like whales or dolphins, aren't furry, so I'd say that while fur may be a net positive for animals that spend some time out of the water, it's probably not because of their time in the water.

It'll increase drag, which means that they have to expend more energy to move through the water.

It might have some insulation benefit, but I'm not sure how significant that is in water, and I'd guess that fat is probably preferable in that case.

My guess is that the main benefit is for outside water.

First, thermal insulation, where the fur limits convection of air, so you get air pockets, which doesn't conduct well.

Second, as a disposable, dead layer, it also provides protection against UV light and such. We don't think of living out of water under the direct radiation from the sun as being particularly difficult or the environment harsh, because we casually do it every day, but it was a very hard problem for life to solve.

https://en.wikipedia.org/wiki/History_of_life

Earth formed about 4.5 billion years ago (abbreviated as Ga, for gigaannum) and evidence suggests that life emerged prior to 3.7 Ga.

So it took less than a billion years for self-replicating life to arise on Earth in the oceans.

But it took about three billion years after that for that life to be able to survive outside of the oceans.

https://en.wikipedia.org/wiki/Ourasphaira_giraldae

Ourasphaira giraldae is an extinct process-bearing multicellular eukaryotic microorganism. Corentin Loron argues that it was an early fungus. It existed approximately a billion years ago during the time of the transition from the Mesoproterozoic to Neoproterozoic periods, and was unearthed in the Amundsen Basin in the Canadian Arctic. This fungus may have existed on land well before plants.

I know that when people are moving dolphins and whales around, they keep them covered, partly to keep them wet, but also because they will suffer badly from sunburn if not done. This dolphin had a lot of its skin get destroyed and fall off its body after being exposed to the sun for some hours:

https://metro.co.uk/2016/07/21/dolphin-suffers-extreme-sunburn-after-getting-stranded-on-beach-6020906/

Can animals get sunburn?

Yes – and marine mammals are more susceptible to sunburn than most other animals, because they don’t have fur, feathers or scales to protect them.

Dolphins and whales rely on being underwater for a lot of the time to combat the effects of the sun. .