exposed doorbell transformer inside a walk in closet
The worst hazard here is snagging your clothes.  The transformer is low-voltage, so you can touch the wires and probably not feel anything.  If your hand was wet, you might get a buzz, but it's not dangerous.

Some transformers can get warm, but doorbell transformers normally do not because they are very low power devices.  You could hang a shoebox on it or otherwise cover it to avoid snags.