You can take a shower during a tornado warning, although it's best to avoid showering or bathing during a tornado warning.
The reason why it's best to avoid taking a shower or bath during a tornado warning is that the tornado warning could possibly turn into a tornado bearing down and you may need to take shelter which can take longer when you're in the shower.
During a tornado warning it's best to wait to shower or bathe and be ready to take shelter if needed and then after the tornado warning has gone away then you can take a shower or bath.
Also stay awake during a tornado warning as you could need to take shelter quickly and you don't want to be asleep when a tornado possibly rips through.
During a tornado warning and other storms there could also be a slight risk of lightning traveling through the water and into the plumbing through the pipes and that would when showering could in rare cases lead to electrocution from the lightning.
Although I have personally took a shower during a tornado watch as well as lightning storms, but when I do take a shower during a tornado warning or lightning storm I take shorter showers and am prepared to take shelter and have my phone alerts and weather radio on listening to the weather.
Most plumbing in houses now is plastic although some houses may still use brass, lead and copper pipes which do conduct electricity.
So it's best to avoid showers or baths during storms including tornado warnings and tornado watches.
But if you absolutely must take a shower during a tornado watch or tornado warning or thunderstorm you should be prepared to take shelter if needed quickly.