1. Does your wallet provide you with the private keys for all addresses contained in it?
Yes? Wallet is OK.
No? Wallet is not Ok.
In the case of Mycelium, the answer to 1. is "Yes". So as long as you are happy to store your coins in a mobile wallet on your phone then whatever happens on August 1st, you will be fine... regardless of which way the Mycelium app developers decide to go. You can easily export your Master Private Key/Seed and use the BIP39 mnemonic code converter (https://iancoleman.github.io/bip39/) to get all your private keys and use whatever wallet you need/want.
If you have access to the private keys, you are good to go regardless of what happens. You can put your private key(s) into "LeftForkWallet"™ and have access to "LeftForkCoins"™... and/or you can put your private key(s) into "RightForkWallet"™ and have access to "RightForkCoins"™
What you DO NOT want to do is put your coins in any online service like an exchange/gambling site/web wallet etc where you do not have direct control over the private keys and are at the mercy of that service as to which way they want to send to your coins.