Nuclear reactors are in a delicate balance, they are in constant feedback loops that means an unexpected power drop or an unexpected rise can cascade. The withdrawal of the others rods is not specifically in response to one being dropped in accidentally - it will be in response to the drop in the power output.

There's not a safety risk from doing this because the control systems are doing this to specifically stay within the stable power output.

There are some significant negative consequences from the power dropping excessively and unexpectedly. One of them is an excessive build-up of Xenon in the reactor which is a feedback loop that continues to reduce fission (known as Xenon poisoning) and is one of the underlying causes of the Chernobyl incident. Now, as far as I'm aware there are no Nuclear reactors running today that are _unsafe_ if they encounter Xenon poisoning - but it's not something you want to stumble into.

If there were a genuine safety concern related to a control rod drop then the reactor would scram and the _all_ the rods would drop and the reactor would need to be restarted.