You have to balance side effects with the beneficial effects of the drugs and each one of us decides what is and unreasonable side effect. For some, methotrexate works so well that they are willing to live with hair loss, but for others, it's an unacceptable side effect.

I would recommend that you talk to your doctor about this - I've heard in the past that increasing folic acid may be helpful in addressing this particular side effect and you could try B12 shots, as it may also help with hair loss. You may also want to discuss treatment options with your doctor in terms of what other DMARDs (disease modifying antirheumatic drugs like methotrexate, Plaquenil and the Biologics) may be available for you.