No, Firefox can not cause bsods and there is nothing wrong with it at all. It only accessed drivers (Realtek most likely) that caused the issue.
No doubt, the latest crash dump shows this:
Code:
Unable to load image rtl8187B.sys, Win32 error 0n2
*** WARNING: Unable to verify timestamp for rtl8187B.sys
*** ERROR: Module load completed but symbols could not be loaded for rtl8187B.sys
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* *
* Bugcheck Analysis *
* *
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Use !analyze -v to get detailed debugging information.
BugCheck 100000D1, {0, 2, 1, a20fc578}
Probably caused by : rtl8187B.sys ( rtl8187B+13578 )
Followup: MachineOwner
--------- You probably chose the wrong update. Like I said, research your hardware until you are sure which update to apply.