Please don't use the object manager in this way :(
Product Page
Assuming you want to use this in a block you should be able to use the registry to get the product.
In your blocks constructor you can include $this->registry = $context->getRegistry();
and then in a method you can get the product and any attribute/data you wish
$product = $this->registry->registry('current_product');
return $product->getData('msrp');
Then from the block template you can call your method that returns the above msrp, eg. $block->getProductMsrp();
Product Listing Page
You should already have a $_productCollection
so you should be able to get the msrp from the products in the collection
<?php foreach ($_productCollection as $_product): ?>
<?php echo 'mrsp below'; ?>
<?php echo $_product->getData('msrp); ?>
<?php endforeach; ?>
Doing the above gives me

If you look in vendor/magento/module-msrp/view/base/templates/product/price/msrp.phtml
you can see how Magento does this around line 48
Worth mentioning aswell that after making your changes you will most probably need to clear caches etc assuming you are working with caches enabled.