How? Do you have a suggestion for raising revenue that's as effective? Lots of nonprofits struggle because they're too afraid to ask people for money but it turns out if you don't ask no one donates.
A pop-up or -under window and a modal dialog are also different in that the modal is confined to the window or tab it exists in and when you leave the page you're on it goes away.
wikipedia has done a lot of research on this. Their method doesn't block content, doesn't force the user to interact with a dialog, and isn't perennial.
If the website is honestly just a bunch of scraped content which solely exists to solicit donations then go ahead. But if there is another purpose, any other one, than the popup dialog detracts from it in an unnecessarily injurious way.
A pop-up or -under window and a modal dialog are also different in that the modal is confined to the window or tab it exists in and when you leave the page you're on it goes away.