The thing is, if everyone ran adblock, I'd have no choice but to require a membership to play Warzone. I know you don't like ads, I don't either, but ads are what enable the site to be free. Therefore, if you're the kind of person who don't want to pay for a website or service, you should be glad that the ads are there as they are what allow you to use it for free.
Keep in mind, every time you use the website it costs money. It costs over $1000 per month to keep the Warzone servers functioning, and that gets paid mostly with advertising revenue.
I try hard to make the Warzone ads as un-obtrusive as possible. If you see one that's interfering with your gameplay, please let me know at https://www.warzone.com/ReportBug