You're still assuming what you're attempting to prove; it's not a useful way to make a case. Why should Egalitarian apply to all sapients?
Because thats what Egalitarian is. The description for Fanatic Egalitarian is:
Beware always those who would be despots, under the false presumption that their desires and agendas are somehow more imperative than those of their fellows. A society that does not see to the needs and rights of all of its members is not a society - it is a crime.
In general that applies univerally. In the specific case of Xenophobes, Aliens/Foreigners/Barbarians are seen as less sapient and therefore not part of society in the same way. That does not mean they have no rights or protections. Indeed, Slaves would often be in similar positions as Women and Children in a household, legally 'owned' by the master of the house but still with their own rights, specific freedoms (like religion) and part of the household. A quote when Athens evacuated once wasto : "save themselves, their women, children, and slaves".
This also fits in the (non-fanatic) Egalitarian description:
Any society that does not embrace equality between its members - where an individual can rise to any position with enough hard work - is not only deeply unfair, but ultimately counterproductive.
Slaves may not be regarded as members of society, but the sentiment of rewarding hard work and allowing a Slave to gain their freedom pervades an Egalitarian veiwpoint. That has been one of the common concepts in Egalitarian societies historically.
Not to mention, we are not refering to an Egalitarian nations ability to select those policies. We are discussing the reaction of members of an Egalitarian faction. Your empire can allow resettlement if they want, it will just annoy the hardcore Egalitarians in the progressive faction, who place more emphasis on their Egalitarian principles than their Xenophobic ones.