DALLAS — Fight or flight?

Those are, in essence, the two very different approaches that the activist community is taking with Exxon Mobil these days.

One group is made up of investors who want to hold on to their stakes in the company and prod the oil and gas giant, through shareholder resolutions and by applying steady pressure, to adopt new policies that reflect the realities of climate change.

The other major group is campaigning to make Exxon Mobil a pariah and is urging big institutional shareholders to dump all their fossil-fuel stocks.

Both groups showed up in force on Wednesday at Exxon’s annual shareholder meeting here. Outside, several dozen protesters waved signs reading “ARREST EXXON” and “KEEP IT IN THE GROUND,” and chanted slogans like “Exxon lies, oceans rise!” and “Windmills, not toxic spills!”