I have all of my credit card statements dates synchronized. I've been doing that since my very first card and whenever I opened new cards, synching the dates would be one of the first things I do along with setting up autopay for full balance each month.
Some banks allow you to change your statement date while some banks only let you change due date whereby you can indirectly change your statement date.
Some have both a fixed statement date (which you can change) and a fixed due date (which you can also change) of each month.
Some have a set number of days between the statement date and the due date (say due date will always be 25 days after the statement date) in which case, if they let you set a due date, your statement date can vary by a day or due depending on which month it is.
I think all banks allow you to change the due date but some banks don't have certain dates available. When I first opened my discover card, they didn't have my synchronized date available as my statement date so I had to call all of my other CCs and change all of their statements dates to match Discover's.
I think banks have policies on how often you can change your due or statement dates within a given time period (6mths). I have hit that limit before but if you talk to the manager, they can change it for you again without any trouble.
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