Is using a new address for each transaction pointless when applied to a donation button on a private website? I'm just looking at how to implement donations on my site and also read that I should use a new address for each transaction to increase anonymity.

Is this an ultimately pointless practice when tied to a single private website?
A new address for each transaction is used for anonymity most of the time. For a donation website this isn't isn't that useful. Most people reuse because they feel that their address could be remembered and identified later on, even though this is hard to do it is possible.

Unless you want it to be hard to tell who and where the bitcoins are, it's better to reuse and not have to have a complex system that generates and keeps track of generated addresses.