I have a Celestial Crusader card that says other white creatures get +1/+1. Does that apply only to my white creatures or will it apply to my opponents white creatures as well?
There are no hidden limitations.
The effect of Celestial Crusader's ability applies to white creatures other than that Celestial Crusader, no matter who controls them.
If it only affected creatures your control, the ability would have been phrased like Paragon of New Dawns's:
Other white creatures you control get +1/+1.
If an effect states "other ~ you control," then it only affects those ~s you control. but if it only states "other ~" then it applies to all that are on the battlefield. a good example is slivers. while Battering Sliver affects all slivers on the battlefield, giving them all trample, Groundshaker Sliver only gives slivers on your side of the battlefield trample.