Can I batch update the tax option for multiple clients?

No. If using both project-level and item-level taxes, then you use the 'No tax on tax' option to prevent double taxation (tax on tax). You can change this setting on individual clients as needed and there is no batch update available on it as of now. You can also choose to exempt the specified client from item taxes, namely Tax 1/2/3, by selecting the 'Exempt client from all taxes' rule.