django_q_xor.py

from django.db.models import Q


def q_xor(*queries: Q) -> Q:
    output = Q()
    for i in range(len(queries)):
        variation = Q()
        for j, query in enumerate(queries):
            variation &= ~query if i == j else query
        output |= variation
    return output

django_xor_usage.py

from django.db.models import Q


class Test(models.Model):
    field_1 = models.ForeignKey(Model1, on_delete=models.CASCADE, null=True)
    field_2 = models.ForeignKey(Model2, on_delete=models.CASCADE, null=True)

    class Meta:
        constraints = [
            models.CheckConstraint(
                check=q_xor(Q(field1=None), Q(field2=None)),
                name='has_field1_xor_field2',
            ),
        ]

migration_operation.py

from django.db import migrations, models
from django.db.models import Q


class Migration(migrations.Migration):
    # dependencies = [...]

    operations = [
        # ...
        migrations.AddConstraint(
            model_name='test',
            constraint=models.CheckConstraint(
                check=Q(
                    Q(Q(('field1', None), _negated=True), ('field2', None)),
                    Q(('field1', None), Q(('field2', None), _negated=True)),
                    _connector='OR',
                ),
                name='has_field1_xor_field2',
            ),
        ),
        # ...
    ]