They could mean the same thing, i.e., if the weather isn't rainy at some point in the future.
We can go for a nice walk as long as it doesn't rain.
We can go for a nice walk as long as it doesn't rain.
But they could also be different as the continuous can refer specifically to an interrupted time.
We can eat in the garden as long as it isn't raining. (i.e, the rain starts before we want to eat)
We can sit on the grass as long as it doesn't rain. (The rain could have finished but the grass would still be wet. Or, it could still be raining at the time.)
To understand this better, the best thing is to study 'aspect' - simple, continuous, perfect and perfect continuous.
The easiest way to do this is to study Narrative Tenses. These are specifically about the past, but the effects of aspect are the same for present and future, too.