If I read the Bitcoin ETF application papers correctly, in the case of a hardfork, BlackRock could choose the suitable network on behalf of their investors.

Given the growing market share for these ETFs, wouldn't this give TradFi institutions a significant influence?

Wealth Management by profession • Crypto and DeFi by passion • Generative AI art connoisseur • Humor is desired

Technically, the custodian's wallet would hold both assets. However, the ETF issuers agreed that they would relinquish any entitlements to a hard fork or airdrops.
The question that remains is, which of the two chains is then considered the "main chain"?

What do you mean with 'choose the suitable network'? Wouldn't they just hold both assets?

All these asset managers are toxic and dangerous entities centralizing voting power and influence over companies AND now crypto. 

Just think about how bad ETFs actually are, as being investors in them, we hand over our voting power to Blackrock et al, who impose ESG BE and stuff

Currently etfs have roughly ~700k bitcoin in them. The good news is at the moment they represent a tiny portion of the holders. This should limit their influence by now, but the way that number is growing it will be a concern in the future.