[Answered ]-Django model query selecting related items and excluding current object

You should work with .annotate(…) to count the number of matching tags:

from django.db.models import Count

article_object = self.object
article_tags_array = article_object.tags.all()
related_articles = self.model.objects.exclude(pk=article_object.pk).filter(
    is_published=True,
    tags__in=article_tags_array
).annotate(
    matching_tags=Count('tags')
).order_by('-matching_tags').prefetch_related()