Assuming that:
... <link rel="stylesheet" href="this_page.css" /> <link rel="stylesheet" href="modal_1.css" /> <link rel="stylesheet" href="modal_2.css" /> ...
Due to the cascading nature of CSS (sorry, I had to) using the same selector overrides any previous styles over and over again. Thus, if modal_1.css and modal_2.css apply the x style to the body tag, for example, the second stylesheet will override the first.
The sad part is that there is no other way out than, as you suggested, changing the two selectors to make them more specific.
Looking to the future, the best way to avoid overriding previously declared styles is to always be specific about the specific element you are targeting and its proper place in the DOM. Note that LESS is just a CSS preprocessor that allows you to use different CSS syntax.
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