Accessibility problem, websites force me to change zoom over and over?

[Cramp!]

I've got some issues seeing the screen clearly, especially with this fashion of making all print super tiny. But lately a new thing is happening.

I go to a site... at my usual 125% setting on zoom.... the site pops up a stupid message like "log in with facebook" or "do you want to chat?" and the x-out is either not visible at all (I mean, they hide it on purpose) or hidden because the zoom level doesn't show it on screen. So I zoom out, and I usually have to go below 100% to x-out, I close the silly message, and zoom back up to 125%.

This is getting annoying.

Any way to stop these annoying messages that disable the page until you close them?