Transaction in an uncle are ignored, if they are valid they may already be included in a parent block, or can be mined in a future block.
Only the header of an uncle block is included in the blockchain. From the Ethereum Yellow Paper section 4.3 The Block.
4.3. The Block.
The block in Ethereum is the collection of relevant pieces of information (known as the block header), H, together with information corresponding to the comprised transactions, T, and a set of other block headers U that are known to have a parent equal to the
present block’s parent’s parent (such blocks are known as ommers).