Honestly, the answer is yes and no. Some street benches get noticeably slippery when wet, while others stay surprisingly grippy. It mostly comes down to the material and the finish.
Smooth painted metal benches are often the worst. When rain hits a glossy painted or powder-coated surface, water can sit on top and create a thin film that reduces friction. If you are wearing smooth-soled shoes, that can feel a little slick. Bare metal without texture can be even worse.
Wood benches are a mixed bag. A smooth, heavily varnished wooden bench can feel slippery when wet, especially if it has several coats of gloss or if moss and algae have started growing on the surface. On the other hand, naturally rough or weathered wood tends to hold traction better because water soaks into the grain or the texture gives your clothes and shoes something to grip.
Plastic and recycled composite benches usually perform better. Many of them have molded textures or a slightly matte finish that does not trap water the same way a glossy surface does. But even those can become slippery if they are dirty or if a lot of pollen, mildew, or grime has built up.
Concrete and stone benches are generally safe in the rain. They are porous enough to absorb a little moisture and rough enough to keep decent grip. The bigger risk with those is staining, not slipping.
So if you are worried about a specific bench, look at the surface. Is it glossy, smooth, or painted? If yes, take a second before sitting or walking on it in wet weather. Most public benches are designed with some texture to reduce this problem, but older ones or cheaply finished ones can still surprise you.
A practical tip: wipe the bench with your hand or a cloth before sitting. Even if it looks damp rather than soaked, that thin layer of water is usually what makes it feel slippery. And if you see green moss, dark stains, or a slimy film, treat it as slick until proven otherwise.