Especially with the massacre of local Christians, as well as Muslims & Jews, when the Crusaders initially captured Jerusalem...
And even if that was no more than "taking a city by assault was never pretty" rather than going out of their way to kill nonCatholics, that was hardly the way to establish that they were welcome as opposed to tolerated.
Even at best Outremer seems to have been seen as no better than a potential counter to another foe - it never had anyone who had some real interest in its survival closer than Sicily (even the Latin Empire was too busy with its own concerns to even care), if that.
This is hardly a unique situation, but whereas
Rūm has the prestige of an old, old state and high sounding titles to hand out - Outremer has nothing of the sort.