How critical is the site's validity for search robots?

The problem with invalid layout is that different browsers can understand it differently. As a result, you will never know whether the search robot correctly understands your invalid layout.

Moreover, the algorithms of search robots are changing. And sometimes there are new ones - the same google once upon a time was an incomprehensible new site... Any new version of the robot will understand the valid layout as it was intended. But with an invalid one, an unpleasant one can come out surprise.

It is necessary to understand that intentionally invalid layout is a crutch. Moving the crutch from the code to the layout-you do not get rid of the crutch, no matter how much you would like to think otherwise.

And you also need to understand that the validity is different. HTML 4.1, XHTML, and HTML 5 are three different standards, and the layout that is valid in one of them will be invalid from the point of view of the other. Therefore, check the site with random web validators, and then immediately rush to fix everything in a row, and the truth is not worth it. Usually it is enough to ensure that your editor correctly highlights the syntax and does not find errors - the latest standard (HTML 5) forgives a lot of layout, and this is documented behavior.

You probably mean by the validity of the code - its correctness. Before the browser displays a web page, it must build the object model of the DOM document.

• The browser reads the original HTML bytes from the server disk or network, and translates them into separate characters based on the specified file encoding (for example, UTF-8).
• The browser converts a string of characters into various tokens - as specified in The W3C HTML5 standard. For example,"", " " - and other lines in angle brackets. Each marker has a special meaning and its own set of rules.
• the emitted tokens are transformed into "objects" that define their properties and rules.
• DOM construction: Because HTML markup defines relationships between different tags (some tags are contained in other tags), the created objects are linked in a tree data structure that also captures the parent-child defined in the original markup: The HTML object is the parent of the body object, the body is the parent of the item object, and so on.

W3 documentation on DOM. This whole process takes some time, especially if we have a large amount of HTML to process. The more code there is, the longer it takes the browser to process it. This affects the page loading speed, which is critical for mobile users - statistics report that they wait no more than 3 seconds, and then leave. And this currently-between 50% and 60% of all traffic on the network. You can see that reading/creating a DOM is a fairly complex process. Now imagine that there is only one error in the source code of the page (not to mention many errors), or even there is a fatal error. You can see how complicated the browser is in this case. The HTML5 standard is quite liberal and the browser can understand the concept of your web page, even if the source code has several errors. But the more errors there are, the more the meaning of the web page concept is blurred and the more time the browser needs. This increases the download speed. Also, multiple source code errors prevent the correct understanding of the web page for mobile users. In addition, structured markup is closely related to the source code. This markup is used for rich search results + for voice search + for machine learning. Finally, source code errors are a violation of the HTML5 standard. As a result only with source code errors you can get: loss of 50% -60% of traffic-mobile users, website problems in the mobile index, browsers and search engines can not correctly understand your site and its structure, lowering the search rank.

How critical is it to have valid HTML, CSS, and JS codes?

The answer to this question can be VERY easy to find yourself. You take sites from the top and check for validity.
And try to find at least one 100% valid one :)

But this does not mean that it is necessary to intentionally allow shoals.

Quite often in articles I meet expressions. "validity for validity's sake "(written with sarcasm)

This is a thick hint that not it is worth licking the validity on an already live site, not originally created by you (all its elements). It is better to give your strength to more productive activities.