Saying that, 'support' completely depends on what the FASTA is and where it comes from (assembly, sequence database, alignment tool, etc), which is something the parser/grammar can't define up front from such a simple format.
Much of the problem comes when validating the sequence for a specific alphabet or symbol set. If the alphabet isn't explicitly defined (again impossible to determine from the format without guessing) then you can certainly run into problems.
This is also an issue when using FASTA for both regular sequence data and for alignments (e.g. length of the sequence would have to take into account possible gap characters generated from various tools like '-?.', or stops in protein seqs like '*').
These are tools that have been in widespread use for ~15 years, so if you have run into problems you should be more explicit in what they are so they can be addressed.