Hi @Magnus137
I don't specifically know the Swedish tax system, but here is how it would usually work:
If cleaning fees go through Airbnb and the Airbnb income is reported for tax purposes, the cleaning fees are included in your revenue (as you have said). When you pay the cleaners, you should deduct the payment as a business expense. Tax is calculated on your profit, so the net amount is the same and you don't pay any extra tax.
The only way it can have a negative effect is if it triggers something that's only based on your revenue. For example, in some countries you have to register for VAT if revenue (not profit) exceeds a certain amount. In theory the cleaning fees could increase your revenue to the point where you have to register to pay VAT, but you would have to do business on a rather large scale for this to happen (and would then likely be liable for VAT anyway - it's unlikely that cleaning fees on their own would push an Airbnb business over the threshold).
So for the vast majority of us there's no downside to receive cleaning fees as part of our Airbnb payout - it makes it much easier to collect from the guests.
(Also, many hosts don't charge the exact cleaning fee that they pay to the cleaners - the "cleaning fee" is often used as a way to charge for guest change-over expenses in general)
Apologies if there's something in the Swedish tax system that works differently - this is a general answer to explain why most hosts don't worry about it.