The National Association of Realtors.That said, I will not be signing an Exclusive Right to Represent as an established real estate investor, and I’m honestly a little annoyed to be asked.I also realize this may qualify for Reddit’s AITAH channel.

You don't have to sign the agreement, though some state laws require an exclusive contract.

Quote from @Victor Yang:In addition, is it possible for me and my wife to gift 36k worth of equity per year of the house (under the annual exclusion limit) and therefore have none of the costs go towards the lifetime gift limit?

For 2024, the annual gift tax exclusion is $18,000 per recipient (rising to $19,000 in 2025), and amounts above this require filing a gift tax return (Form 709).

I have bought 2 rental properties and seen other realtors, and I have never once been presented with an exclusive buyers agreement.

Just be mindful that you can't 1031 a personal residence but it might be eligible for capital gain exclusion from section 121.

Any amount above the annual gift tax exclusion ($17,000 for 2023) counts against your lifetime exemption.

The capital gains exclusion is available to owner occupants primary residence.

Does renting the home while deployed void the eligibility for exclusion of gain, even when the home was lived in/primary residence for 2 of the last 7?  

They used to offer exclusive properties but now it appears that they are pulling MLS listings and will connect you with an agent.