Foam screens (sometimes called “clown noses”) for microphones are primarily for controlling wind noise when singing outside. When the wind blows across a mic, it makes a rumbling sound that is distracting and annoying. Indoors, they aren’t really needed unless you have fans blowing air around the singer. The other purpose of the foam screen is to keep spit and bits of food out of the microphone, since it is far cheaper to replace a bit of foam than to replace a microphone. The latter is more important for publicly used mics, like in a karaoke bar or at some churches.
But do the foam screens make the sound “muddy”? They are supposed to be acoustically transparent, but will cut a certain amount of the high frequency sound. Some EQ settings may need to be compensated if using one. It is best to adjust these settings at a sound-check before a show. Typically, a muddy sound comes from not cutting the low range (below 80Hz) on a microphone. Most mixer boards come with a low-cut switch (or high-pass switch) designed just for this. Always engage this switch for a singer’s microphone.
Foam windscreens are not really designed to control plosives and sibilance (loud “P” sounds and hissy “S” sounds), though they can help a bit. It is better to use techniques like speaking over the mic instead of directly into it for certain words.
Some simply don’t like the appearance with the foam cover. Some feel it ruins the sound entirely, some feel it cuts off too much of the high end. I think a lot of these reactions are emotional rather than factual. I’ve only seen one graph that shows a tiny bit of high frequency being cut by the foam screen.
But the short answer is to only use a foam windscreen on a singer’s microphone is outdoors where wind noise is a problem, indoors where fans are blowing air across the singer, or possibly anywhere the mic is shared a lot and may get crud on it. For most indoor gigs it isn’t needed.