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> Is there any disadvantage of doing it this way that I should be aware of?

In general whitelisting is the best way to sanitise, but it does create important error classes, especially missing items. I think that your list of `allowedNodeTypes` could be better ordered to allow manual checking (e.g. `'strong'` and `'b'` are together, but `'em'` and `'i'` are not), and it's not obvious that the omission of `'h6'` was intentional.

Is there some HTML spec which adds an `<italic>` tag?

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> The idea is to safely copy content from a site but apply my own style-sheet

In that case, shouldn't `<font>` get special treatment?

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>     				let element = document.createElement(keep_tags?tag:'span');

This seems to alias the name of the DOM class `Element` - or, at least, my editor's JavaScript highlighting thinks so. Maybe rename it to `child2`?

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>     					for (var name of child.attributes){

Why `name`? That looks like something that was written when you expected the iterator to give you names instead of nodes and wasn't corrected when the body of the loop was.

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>     						if (urlTransformAttributeTypes.indexOf(name.nodeName)>=0){
>     							element.setAttribute(name.nodeName, new URL(name.value, 'https://target_site.com/folder/'));
>     						}
>     						else if (allowedAttributeTypes.indexOf(name.nodeName)>=0){

This is the only usage of `allowedAttributeTypes`, and it's only used if the name wasn't found in `urlTransformAttributeTypes`.  Therefore it's inefficient and confusing to have some names present in both.