We of the Scions Hospitalier stand firm in the face of Adversity!
We are they who shall perfect the Emperors Vision for a Humanity Ascendant!
No Xenos, Traitor or Mutant* Shall stay our Wrath!
Our Judgement shall be vicious and brutal! They shall earn no Quarter, no Respite!
They who would bring low the Vision of the Emperor (Mighty is He!) shall be Eradicated! No Trace Shall Remain!
*Terms and conditions may apply (Navigators)
Our Friends and Allies need not fear us! No man shall be left behind!
No Mortal need revere us! For We were Human And Through our craft will Humanity in its entirety be Uplifted!
In More General, less Preachy-Prayer-y way, The Scions Hospitalier and Pionus would initially be disbelieving (like many) or the Initial Berayal but, as information would come in, would lock their jaw, grit their teeth and set about annihilating the enemies of the Imperium.
They would use any genetic information gathered from their Apothecaries who were previously attached to the Traitor Legions to use any flaws to their advantage. They would also study in detail the minutiae of the traitors. They would perform tests on the few they capture to make more and more efficient ways to kill them.
Their Specialty for Void Combat they would use to the maximum seeing as no other legion besides the Drowned had a Specialty in the field. Instead of Boarding enemy Ship and fighting on their home turf, they would sabotage the exteriors such as the Engines, Weapons Batteries, Docking Bay Doors. They would disable and render helpless before evacuating the vessel and Vaping it with their own ships-to-ship weapons.
Their Homeworld of Iona would be all but unassailable due to its Nature as a Water World making conventional assaults all but impossible and the Space Installations in system being crewed by void-specialized Astates meant that any combat occurring in and around the system very difficult for the Traitors to gain any lasting ground.
They would start fighting Traitors with any means necessary: Phosphex, Rad Weaponry or anything that they would never normally use for standard combat, Using Scorched Earth tactics on any Traitor Aligned Worlds deeming them nonredeemable, consigning any Traitor Recruiting worlds to Exterminatus.
On the Other Hand, would they be on the defensive, they would adopt a more extreme "No Man Left Behind" mentality going out of their way to ensure successful Mortal (non-Abhuman) and Fellow Loyalist retreats.
However, they would also become much more Reserved with fellow Loyalist Legions being wary that any of them might join the traitors at any point. The only Imperial Institutions they would remain open with would be the Adeptus Custodes or any that would fall under the direct jurisdiction of the Emperor or Malcador. This reservation would even extend partially to the Mechanicum though not as strongly.
S'all I've got atm.