Yes, Castilleja are difficult to identify and there are also a lot of hybrids in some areas (in the mountains here, for example). According to Wildflowers of the Pacific Northwest (Turner and Gustafson), the species whose flower colour ranges include orange, that occur in the Mt. Rainier area are C. hispida, C. miniata and C. rupicola. All 3 are described as possibly having lance-shaped leaves.
Do you have any closer photos of the same plant?
Both C. rupicola and C. hispida usually have lobed upper leaves; I can't see that on your plant (though a closer photo would help), so, sure, could be C. miniata?
