It's not quite as alarming as it might feel at first. Data breaches happen to big organizations all the time, and while it's annoying, the RNLI is being pretty transparent about what happened and what they're doing to fix it. The key thing is that they're notifying people, which means you can actually take steps to protect yourself rather than discovering months later that something went wrong.
If you've donated, start by changing your password on the RNLI website if you have an account with them. Make it something strong and unique - not something you've used elsewhere. Then keep an eye on your bank or card statements for the next few months. Most donors won't see anything suspicious, but it's worth watching just in case. You might also get emails trying to phish you with fake RNLI links, so be careful about clicking anything that looks even slightly off.
Beyond that, the standard stuff applies: consider freezing your credit if you're really worried (though it's probably overkill here), don't click on unexpected links claiming to be from the RNLI, and ignore anyone asking you to "verify" your details via email. The organization has already said they're working with security experts, so they're handling their end. Your job is mainly just being aware and not falling for follow-up scams that criminals might try once they know you're a supporter.