I am not native English speaker but for me ostracizes are evil and ostracizing has really distinct feel to it.

Not accepting someone into group for me does not fall under 'ostracizing' - for me ostracizing is not accepting someone into the group and making such person feel worse and even feel attacked.

Not accepting Joe Badbreath to the "Fresh Teeth" group and letting him know "Hey Joe, you don't belong here because X" for me is not ostracizing.

Not accepting Joe to the group by "we don't accept smelly people here, go away you XX" and then mocking smelly people in the group regarding them as lesser people. - that is ostracizing for me.