Magento – Hide breadcrumbs on specific category page in magento2

You can rewrite the category view block and remove the breadcrumbs block if the display mode is PAGE For this create a new module. ([Namespace]_[Module]). Here is what you need.
app/etc/modules/[Namespace]_[Module].xml - the declaration file

<?xml version="1.0"?>
<config>
    <modules>
        <[Namespace]_[Module]>
            <codePool>local</codePool>
            <active>true</active>
            <depends>
                <Mage_Catalog />
            </depends>
        </[Namespace]_[Module]>
    </modules>
</config>

app/code/local/[Namespace]/[Module]/etc/config.xml - the configuration file

<config>
    <modules>
        <[Namespace]_[Module]>
            <version>1.0.0</version>
        </[Namespace]_[Module]>
    </modules>
    <global>
        <blocks>
            <catalog>
                <rewrite>
                    <category_view>[Namespace]_[Module]_Block_Category_View</category_view>
                </rewrite>
            </catalog>
        </blocks>
    </global>
</config>

app/code/local/[Namespace]/[Module]/Block/Category/View.php - your new block

<?php 
class [Namespace]_[Module]_Block_Category_View extends Mage_Catalog_Block_Category_View {
    protected function _prepareLayout() {
        if ($this->isContentMode()){ //if PAGE display then remove the breadcrumbs
            $this->getLayout()->getBlock('root')->unsetChild('breadcrumbs');
        }
        return parent::_prepareLayout()
    }
}

[EDIT] If you want to control this at a theme level you can try this.
Add in your layout file of the desired theme, this xml section:

<catalog_category_default>
    <reference name="category.products">
        <action method="setCanRemoveBreadcrumbs"><param>1</param></action>
    </reference>
</catalog_category_default>

Then the block described above becomes:

<?php 
class [Namespace]_[Module]_Block_Category_View extends Mage_Catalog_Block_Category_View {
    protected function _prepareLayout() {
        if ($this->getCanRemoveBreadcrumbs() && $this->isContentMode()){ //if PAGE display then remove the breadcrumbs
            $this->getLayout()->getBlock('root')->unsetChild('breadcrumbs');
        }
        return parent::_prepareLayout()
    }
}

I'm trying to solve a similar issue, so I'm reading through the code pretty extensively to get to the root of this. I'll start at the end and work backward:

The call to addUpdate() you reference actually does end up calling addUpdate() on the \Magento\Framework\View\Model\Layout\Merge class. Hold onto your seat: it's a bumpy road. The $page variable is an instance of \Magento\Framework\View\Result, and it inherits the definition of addUpdate() from its parent class Layout (in the same namespace). That class in turn calls addUpdate() on a ProcessorInterface, whose default implementation is none other than: Magento\Framework\View\Model\Layout\Merge.

So then to your question about it seeming to pass the entire XML string: you are correct, and the behavior is correct. The Merge class should theoretically be taking care of parsing the <update> inside _fetchRecursiveUpdates() and then loading the layout XML from the referenced handle.

The catch is that _fetchRecursiveUpdates() is never called on XML chunks that are added via addUpdate(). They are assumed to be ready-to-go (non-recursive) layout instructions. Layout XML from external addUpdate() calls are included directly via a call to $this->asString() at the very end of Merge::load(). They never pass through the inner _merge() function which is what indirectly calls _fetchRecursiveUpdates().

A simplistic solution would be to create a new class that extends the built-in Merge class and set it as the preferred implementation of ProcessorInterface. You would then change the addUpdate() method to perform the same logic as _fetchRecursiveUpdates() before saving its argument to the internal array, something like the following:

public function addUpdate($update)
{
    $updateXml = $this->_loadXmlString($update);
    if (strtolower($updateXml->getName()) == 'update' && isset($updateXml['handle'])) {
        $this->_merge((string)$updateXml['handle']);
    } else {
        $this->updates[] = $update;
    }
    return $this;
}