Given the following model with two many-to-many relations:

class Child(models.Model):
    name = models.CharField(max_length=80)

class Foo(models.Model):
    bar = models.ManyToManyField(Child)
    baz = models.ManyToManyField(Child)

This gives the error:

accounts.foo: Accessor for m2m field 'bar' clashes with related m2m field 'Child.foo_set'. Add a related_name argument to the definition for 'bar'.
accounts.foo: Accessor for m2m field 'baz' clashes with related m2m field 'Child.foo_set'. Add a related_name argument to the definition for 'baz'.

Fine; I don’t need the backwards relation. According to the Django docs for related_name (which is only under ForeignKey as far as I can see), I can set related_name="+" and backward relations won’t be created:

class Child(models.Model):
    name = models.CharField(max_length=80)

class Foo(models.Model):
    bar = models.ManyToManyField(Child, related_name="+")
    baz = models.ManyToManyField(Child, related_name="+")

This doesn’t work though:

accounts.foo: Accessor for m2m field 'bar' clashes with related m2m field 'Child.+'. Add a related_name argument to the definition for 'bar'.
accounts.foo: Reverse query name for m2m field 'bar' clashes with related m2m field 'Child.+'. Add a related_name argument to the definition for 'bar'.
accounts.foo: Accessor for m2m field 'baz' clashes with related m2m field 'Child.+'. Add a related_name argument to the definition for 'baz'.
accounts.foo: Reverse query name for m2m field 'baz' clashes with related m2m field 'Child.+'. Add a related_name argument to the definition for 'baz'.

What do I need to do to avoid creating reverse relations?

I think you need to just give the two fields different related_names:

class Child(models.Model):
  name = models.CharField(max_length=80)

class Foo(models.Model):
  bar = models.ManyToManyField(Child, related_name="bar")
  baz = models.ManyToManyField(Child, related_name="baz")

If you don’t give a related name, then it’s trying to create the same accessor name (foo_set) twice on the Child model. If you give the same related name, it’s again going to try to create the same accessor twice, so you need to give unique related names. With the above code to define your models, then given a Child instance c, you can access related Foo objects with c.bar.all() and c.baz.all().

If you don’t want the backwards relations, then append a + to each of the (unique) related names:

class Foo(models.Model):
  bar = models.ManyToManyField(Child, related_name="bar+")
  baz = models.ManyToManyField(Child, related_name="baz+")

You haven’t read Django’s documentation carefully enough. Here it says:

If you have more than one ManyToManyField pointing to the same model and want to suppress the backwards relations, set each related_name to a unique value ending with ‘+’.

The related_name attributes have to be unique, not the same.