Converting aligned fasta to plink ped/bed

An alignment can be the result of two slightly different analyses:

There is multiple sequence alignment (which is what you get from MAFFT) where sequences are aligned so that similar regions are on top of each other. This may require introducing indels (insertions / deletions) if a particular region is absent in some of the sequences.
Then there is alignment to a reference sequence. This is usually how you get variant data and most of the tools deal with this use case. Therefore, in the link you provided the solution includes aligning the data to a reference sequence. Usually the refernce sequence is much larger (e.g. the human genome) and after alignment the result is a file (.bam) that tells you where the query sequences match in the reference.

I did a quick search for ways of converting a multiple sequence alignment (MSA) to VCF. There is a tool called msa2vcf in the Jvarkit collection of utilities that can do this. The example is for the CLUSTAW format but FASTA is accepted as well.
You shoud check that indels were treated correctly because these are most likely to cause trouble. Then you can simply convert the VCF to PLINK format using PLINK.