Your perception of the plastic causing problems is due to the older vinyl flips that would degrade and literally impart a green slime on a coin. The plastic in Dansco or Intercept Shield albums is chemically inert. The plastic will not cause problems.
Dusty mentioned Dansco. They are a fine album, but be aware that they are not all created equal. Older Dansco albums (even new ones from older inventory) will not have the same protection as Intercept Shield albums. (Dusty, you wouldn't be able to tell the difference between the two.) But with Intercept Shield, there is a chemical in the cardboard page that prohibits the sulfur in the paper from reacting with the coin. When you see coins that have been stored in older Dansco albums, you will notice a "halo" on the coin's rim/edge. This "halo" is caused by toning due to the interaction of the sulfur in the cardboard page. Not a big deal, but the Intercept Shield only costs a few bucks more.