Google Tag Manager. How to prevent custom tags from being loaded programmatically?

I think it can be done. Looking at the GTM code, we can see that it uses the insertBefore function to add a Script element to the website (for now, they can change this at any time). So in theory you could "add" some code to a native function and prevent the script from being loaded from a specific source. For example, you can run the following code before loading GTM:

Node.prototype.insertBefore = (function() {
    var cached_function = Node.prototype.insertBefore;

    return function(script) {
        if(script && script.src.indexOf("www.somesource.com/script.js") !== -1){ //change to src you don't want to load on your page
            return false; //don't add the script
        }else{
            var result = cached_function.apply(this, arguments); // use .apply() to call native function

            return result;
        }
    };
})();

(code from: adding code to javascript function programmatically )

I haven't tested this code, so I don't recommend doing it without proper testing, or you might decide not to do it at all (before you start, you might want to read: Why extending native objects is a bad practice? ). I agree with Eike's answer, but I would say that it is possible to prevent custom tags from loading programmatically.