What led to decline in union membership in the early 1900's?
It did not decline.
Our nation as a whole during the period 1900 - 1910 was undergoing a change at the union level. The Knights of Labor were in fact losing membership but this was because they organized by industry without recognizing individual labor groups within that industry. In their place the newly founded American Federation of Labor (AFL) was stepped into the breach.
The AFL was taking over the K of L members but organizing them according to the skill they possessed. When the K of L struck it did so against an entire mill whereas AFL strikes general were about one small group of workers in a factory. But both of these organizations were only interested in skilled labor.
But also during this period another new union came into being, the Industrial Workers of the World. The IWW was different from both of the previously named groups because they took on all workers, skilled and unskilled. It also readily accepted women into its ranks, something neither of the previous groups had done.
Only the IWW allowed its members to remained in good standing when their members failed to pay dues. The AFL required dues of all members on a regular basis. In the early 1900s a few pennies bought bread and milk, staples, and where so many workers were attempting to live on starvation wages, even the smallest unions dues could prove to be unattractive and keep membership down.
Union membership overall did not decline during the first decade. But once the great textile strike of some 30,000 workers in Lawrence Massachusetts was successful, followed by another large and successful strike in New Jersey, union membership grew at a rapid rate.