What I do to bypass this issue is to place the document that contains hyperlinks to a new document or create a new text frame in the pasteboard of the existing document I am working on and place the text in the text frame.
When placing, I make sure the "Show Import Option" is checked and then I use the "Preserve Styles and Formatting from Text and Tables" option.
This will keep all hyperlinks in the text I want to copy. Before I copy, I ensure that I apply the Paragraph style I want to use on the text and put it to the font size if it is not in the original font size of the syle. This is to ensure that the hyperlinks remain highlighted.
What I do to bypass this issue is to place the document that contains hyperlinks to a new document or create a new text frame in the pasteboard of the existing document I am working on and place the text in the text frame.
When placing, I make sure the "Show Import Option" is checked and then I use the "Preserve Styles and Formatting from Text and Tables" option.
This will keep all hyperlinks in the text I want to copy. Before I copy, I ensure that I apply the Paragraph style I want to use on the text and put it to the font size if it is not in the original font size of the syle. This is to ensure that the hyperlinks remain highlighted.
I hope this helps.