Every TE is going to look for WR money, claiming they're a WR. The NFL and the NFLPA are going to have to come to an agreement on how to treat this case, because it will be a landmark decision that affects cap space immensely.
I'd imagine nearly every player is going to look for as much $ as they can get. However the eligibility for tags is clearly set out in the CBA. This only applies to players who can show that they played most of their plays at a different position than the one teams are trying to tag them at. It will have no effect on players that aren't tagged and nearly no effect on the league salary structure. There just aren't that many players that play most of their plays at a position other than the one they are tagged for.
The language in the CBA is about as clear as legalese can possibly be.
"The Exclusive Franchise Tender shall be a one year NFL Player Contract for (A) the average of the five largest Salaries in Player Contracts for that League Year as of the end of the Restricted Free Agent Signing Period that League Year, as set forth in Article 9, Section 2( e),
for players at the position (within the categories set forth in Section 7(a) below) at which he participated in the most plays during the prior League Year, or (B) the amount of the Required Tender under Subsection (a)(i) above, whichever is greater."
Obviously many players play different positions during the course of a game/season. The language of the CBA breaks down position based on individual plays. A player not lined up right next to the T or 1 yard back from right next to the T is not playing TE on that play. If the player is split out then he's playing WR on that play no matter what it says on the team depth chart.