In Apple Pages, how can I disable italic swashes?
You cannot disable these swashes using the Smart Swashes section in the Format » Font » Show Fonts » Typography… window, because they're not Word Final Swashes. Those are disabled by default anyway.

What you're seeing are Line Final Swashes, applied only to the end of a line or a text run with consistent formatting.





I found no option to disable them from the Typography window or any menu option.

What seems to work is to end a line by pressing Shift-Return instead of Return.



Note that this will not end the paragraph and allow you to apply a different paragraph style to the second line, so depending on your circumstances (e.g. use in Headings), this will not be an optimal solution.

You can, for example, make the next line font size 1 and only insert a single space character. In the following example, I entered a single A character of font size 1 to the next line so it's visible as a black dot:



It's an ugly hack, but it might work for you.