Freezing your sourdough starter will generally not harm the starter if done correctly. Some yeast in your starter may die off, but there will be more than enough that survive to get your starter active again once it has defrosted.
If your sourdough starter is less than a few months old, then freezing is not recommended. The yeast and bacteria will not yet have developed enough strength to survive the freezing process.
You can think of freezing your sourdough starter as putting it into hibernation until you want to use it again. And then once it’s revived, it will return to normal within a few days at the most.
Another alternative way to store your starter is to dry your starter and store it in a cabinet. This is an excellent long-term storage solution for your starter, as it can last years like this! In fact, a starter that has been dried can be stored like this indefinitely.
If you want to store your sourdough starter for a longer period of time, such as a few months to a year, then freezing it is a good option.