The most immediate issue is galling. Stainless steel typically contains a lot of suspended carbides ie very hard particles in a soft matrix. This means that stainless threads are prone to galling and seizing.
This is further exacerbated with aluminium which is a relatively soft metal but with hard surface oxides also the difference in hardness between stainless and aluminium means that there is a big risk of deforming aluminium threads and although galling is a specific issue with stainless/stainless threads the relative softness of aluminium alloys means that lubrication is important even if you don't get actual galling per-se.
Even if the thread doesn't actually seize aluminium threads have a much lower load capacity than steel ones so lubrication will reduce the risk of tearing out the threads before the required torque is reached as the applied torque is a function of friction between the threads as well as the tension in the fastener.
Screw thread tend to have a very small area of contact between the mating surfaces and what can happen is that this creates local high pressure areas which strip off the surface oxides and defectively allow the two metal surfaces to weld to each other.
Copper based greases tend to be the most effective for alleviating this.
Galvanic corrosion is also a significant issue in this context but has already been well covered by another answer.