Use CommonMark parser for Markdown
Markdown is a simple markup language to add formatting to plain text documents, which can be easily parsed to convert to HTML or other rich text formats. It is popular on coding websites.
As there was no official standard, different websites developed their own Markdown "flavours", which use different syntax and support different features, and are therefore incompatible with each other.
Now there is an (unofficial) standard, in the form of CommonMark. CommonMark is used by many websites, including GitHub, who rewrote their Github Flavoured Markdown parser to be based on CommonMark.
Problems with the current parser
The current Markdown implementation on MuseScore.org is quite buggy and lacks support for various Markdown features. Swapping to a CommonMark-compliant parser is likely the quickest way to fix the issues.