I would think cedar would last fairly long without the use of linseed oil. One problem with linseed oil is that it does indeed promote fungal growth. Another issue is the type of linseed oil you use. If I were going to use linseed oil (and I never have), I would look long and hard to find a raw linseed oil, or even substitute food grade flax oil, because the processed linseed oils (often referred to as boiled linseed oil) that are not raw generally have some petroleum distillates added to them. You don't mention if the raised beds ever might be used for growing edible crops of any kind, but if they would be, that's the reason you'd want to avoid the boiled linseed oils that have petroleum distillates added to them because those additives can leach heavy metals into your soil.

I know that linseed oil is a popular recommendation for preserving wood used to make raised beds in a natural and eco-friendly way, but I've never seen one bit of research that says it makes the wood last longer in raised garden beds. In fact, I know that I have read before on some university websites that research indicates the linseed oil does not prolong the life of the wood. Based on that, linseed oil seems to me like an added expense that doesn't add value.