Try removing the extra {{...}} tags and the "..." quotes around request.build_absolute_uri, it worked for me.
Since you are already within an {% if %} tag, there is no need to surround request.build_absolute_uri with {{...}} tags.
{% if 'index.html' in request.build_absolute_uri %}
hello
{% else %}
bye
{% endif %}
Because of the quotes you are literally searching the string "{{ request.build_absolute_uri }}" and not the evaluated Django tag you intended.