Usually this is made by combining an 'é' with a '\u0323' under dot diacritic
However, that isn't what you have here:
'ẹ́'
that's not U+0065,U+0323 but U+1EB9,U+0301 - combining an ẹ
with an acute diacritic.
The usual solution would be to normalise each string (typically to Unicode Normal Form C) before doing the comparison.
I don't just want to match e. I want to match all combinations
Matching without diacriticals is typically done by normalising to Normal Form D and removing all the combining diacritical characters.
Unfortunately normalisation is not available in JS, so if you want it you would have to drag in code to do it, which would have to include a large Unicode data table. One such effort is unorm. For picking up characters based on Unicode preoperties like being a combining diacritical, you'd also need a regexp engine with support for the Unicode database, such as XRegExp Unicode Categories.
Server-side languages (eg Python, .NET) typically have native support for Unicode normalisation, so if you can do the processing on the server that would generally be easier.