The XHTML and CSS validators will validate against the corresponding specifications of the W3C standards. Ignoring these mean that your page(s) are deviating from those standards.
Web browsers aim to implement these standards, so ignoring a warning is likely to cause issues on at least some browsers. Therefore, you cannot ignore any warning that the validators give.
Also, having XHTML and CSS conformant web pages is not guaranteed to work on all browsers and be compatible with them as the browsers may implement something differently or incorrectly.
Having conformant pages is still a good thing, as most browsers are (for the most part) conformant and having more conformant pages helps put the ownership on the browser implementers. That is, you (as a web page author) need only concern yourself with being standard compliant. If a browser can't handle that, the issue is with the browser, not the web page author.
If you want to be compatible with a large number of browsers, start with the valid conformant page and then add the minimum needed to get it working on other non-conformant browsers. Doing it this way is a lot easier than starting with a non-conformant page and trying to make that work on most browsers.