Is it mandatory to specify entry criteria for a workflow?

No, it is not mandatory. Entry criteria are required only when you want to filter records. You can also leave the Entry Criteria field blank.
For example, you can specify the criteria to send a thank you email to all the leads who subscribe to email marketing on the current date.
In this case, you can specify Email Opt-in has changed to Double Opt-in and Subscription Date equals Current Date as entry criteria.