You subtract the taxes specific to the industry. Not all their taxes. Are there any such taxes?

I subtract all their taxes. If Exxon pays $100bn/yr in various normal taxes, and the government pays them $1bn/yr in fossil fuel subsidies, that's a net subsidy of -$99bn/yr.

How can it be a fair representation of their situation to only say they receive $1bn/yr in subsidy?

Because something like income tax is a given. We're not comparing against a world with no government. We're comparing against a situation where they get no special attention. You can use whatever word you want for it, but if a company pays half as much tax as everyone else that's a big deal.

You're right to say that it's not fair to only list the $1bn. It should be put in context of the $100bn of normal taxes. But reducing it to "$99bn" is not a fair representation either. It doesn't tell you if they otherwise would have paid 100 or 200.

I'm quite happy to accept the reporting of both gross taxes and gross subsidies. My objection is to only comparing the gross subsidies.