Let me begin by saying that generally inline styles can be overridden:
.override {color:red !important;}
<p style="color:blue;">I will be blue</p>
<p style="color:blue;" class="override">But I will be red</p>
This behavior is described in W3 specs, where it is stated that !important declarations do not alter the specificity, but rather take precedence over "normal" declarations.
That being said, when conflicting rules both have the !important flag, specificity dictates that an inline rule is applied - meaning that for OP's scenario, there's no way to override an inline!important.
You can see this example! There are several rules for CSS selector. The strongest selector is inline (if same level with/without !important). Next ones: id, class, etc. So if a tag is already stylized by inline css with !important, you just have a way: use Javascript to change.
var pid = document.getElementById('pid');
var button = document.getElementById('button');
button.addEventListener('click', function(){
pid.style.color = '';
});
p{color:violet !important;}
*{color:blue !important;}
html *{color:brown !important;}
html p{color:lighblue !important;}
.pclass{color:yellow !important;}
#pid{color:green !important;}
<p class="pclass" id="pid" style="color:red !important;">
Hello, stylize for me !
</p>
<button id='button'>Change color by JS</button>
As you see, the style by inline css was removed and the id is the strongest selector now !