You can use the FastaVariant class in the pyfaidx module if you're comfortable with a bit of Python. Sounds like you want something very specific so a script might be your best option.

The simulation tools that are part of RTG Core should let you do this, depending on exactly what you want. E.g:

# RTG commands use a formatted structure (SDF) for random access to parts
# of the data, so format the reference
rtg format -o reference.sdf reference.fasta

# Annotate your population VCF with allele frequency information from the
# samples (if it doesn't already have it)
rtg vcfannotate -i input.vcf.gz -o popvariants.vcf.gz --fill-an-ac

# Generate a new VCF sample column, randomly generated based on allele
# frequency information in the population vcf, plus an SDF containing the
# genome of that individual
rtg samplesim -t reference.sdf -i popvariants.vcf.gz -o pop_plus_synthetic.vcf.gz --output-sdf synthetic_ind.sdf --sample synthetic_ind

# Extract FASTA from the SDF
rtg sdf2fasta -i synthetic_ind.sdf -o synthetic_ind.fasta.gz

The defaults assume a diploid organism, so the output will contain two copies of each chromosome. If you want to get fancy, you can configure your reference with information about autosomes/sex chromosomes and you will end up with the appropriate sequences in the output. We use these tools for simulating small populations/pedigrees of human genomes, including random population variants (popsim), founder individuals (samplesim), offspring (childsim), and de novo variants (denovosim).

If there are multiple variants at a position then it will randomly select one of the alleles or genotype calls. See the caveat section: https://www.broadinstitute.org/gatk/gatkdocs/org_broadinstitute_gatk_tools_walkers_fasta_FastaAlternateReferenceMaker.php

Just adding it here for reference:

bcftools consensus will do the job for SNPs and InDels