This is an old chestnut which crops up from time to time. People tend not to cut grass in the rain for two very important reasons, which I will touch on at the end.
Of course, if cutting grass in the rain was harmful to the grass itself, farmers would have to rush out to their herds of cattle and flocks of sheep, and gather them into their barns in order to protect their pastures from the damage that would ensue if their animals stayed outside.
Unsurprisingly, this is not the case at all. As I intimated at the beginning, there are two very important reasons that people don’t cut grass in the rain.
1/. They don’t like cleaning the mower off afterwards, and
2/. They don’t like getting wet.
Having said that, and on a serious note, you should keep off wet lawns (whether it’s raining or not) particularly if you have a heavy soil, to avoid potential compaction problems and to avoid churning up the levels. If you’ve ever had to repair cattle damage to a lawn, you’ll know what I mean !!