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.

“as long as it isn’t raining” is in the current moment. “as long as it doesn’t rain” is about the future. You are hoping that at some point in the future it doesn’t rain.

Rather than "as long as it isn't raining" I suggest, in most cases, "while it isn't raining". Consider the sentence "The cat is happy outdoors as long as it isn't raining". That is a timeless statement. It has nothing to do with past, present, or future. It's just a statement about the nature of the cat. This suggests to me that "as long as" is an expression that actually has no relationship to time. In situations where you do want to talk about time, use "while" instead. I would say the same for "as long as it doesn't". It is confusing. If you really are interested in time, use a different word. However, it works well for "The cat is happy outside so long as it doesn't rain", a timeless and undeniably true statement.

both are correct, the first means the process, the second means the situation

as long as it isn't raining - present as long as it doesn't rain, - hypothetical future