I know that you’re not supposed to run from shul, but what if it’s raining?
Shalom Eliezer, The Shulchan Aruch (Or. Ch. 90, 12) says you're not supposed to run from shul because it looks disrespectful and like you want to run away from davening. But the Aruch Hashulchan points out that when others can tell that you're running for another reason (for example, if davening isn't over yet and you're hurrying to the bathroom in order to hurry back), it's no problem. Similarly, when it's raining, everyone knows that you're running in order not to get drenched, so it doesn't look disrespectful and is allowed. With Love of Israel, Rav Ari Shvat