Is there network split risk for Taproot activation with two releases (Bitcoin Core and Bitcoin Taproot)?
No. With a softfork, a network split is only possible if miners create invalid blocks. This is something they can do with or without a softfork, so it is not an issue specific to softforks.
It is important for the economy to use their own full nodes to avoid the risk of being led off by a miner attack in the form of invalid blocks. This remains true with softforks, where upgrading is necessary to retain full node security.