Sister lives with Dad no rent all bills paid. She works 3 days month and gets disability. Dad has COPD he does not need a babysitter.

Honestly, as long as I didn't have to do it...I am good. If all she wants is $300 a month, I wouldn't worry about it. It really is up to your father, his money, his choice.

From what you say it seems your sister provides 18 meals a week. Possibly she also does all the housecleaning other than laundry? Handles his medication management? Does his Bookeeping/bill paying? Helps him dress if needed? Provides transportation services when he goes places? Manages household maintenance scheduling when things need fixing etc. Depending on all the things she does that maybe folks don't notice she does the $300 may be kinda cheap?

$300 is well below the amount of money she can earn while on disability. She’s allowed to earn $1220 a month while on disability.

"She also needs to look to her own future. I’m suspecting that a position as a paid caretaker might disrupt her disability income."

That is a good point. Does Sis think when her disability worsens that you will take on the role of Caregiver? Because I doubt if she has money for Caregivers. There is Medicaid homecare I guess. I would make it plain to her that not even consider u caring for her. If she is receiving SSD, there is a limit in what she can make. Also, what is she going to do when Dad passes. I hope not feel you do for her what Dad is. Because he is doing her no favors.

If I were you and made any suggestion to either dad or sis it would be that a care contract be drawn up that includes all that sis is to do for her pay.
Dad’s needs will increase in time and a person there 24/7 is invaluable to the elder. While he is competent at this point, one fall or stroke can change everything. There is a comfort in having someone there regardless of what they do as long as not abusing the home or elders but a contract that lists what’s expected from each could be beneficial.
I would explain that room and board comes with actually doing those tasks and that it protects dad from being penalized from the appearance of gifting his funds should he ever need to file for assistance through Medicaid. The price of facility care will wipe out many if not most elders savings in short order so whether he thinks he will need it or not, it’s more prudent to plan on needing it.
Spend some time looking at care contracts. There are many threads on this site discussing them. If sis doesn’t want to do certain tasks then someone will need to and funds will need to be available. Also remember that she can’t be asked to leave without considering her tenants rights. I’m sure the last thing your dad wants or needs is discord in the home.
So a middle road just might be the contract.
Who is his POA? That should also be addressed.
Look at her raising this question of compensation as an opportunity to get things in order for dad going forward. A trip to a certified elder attorney might help at this point.
And just one more thought. I would consider taking dad and sis on the appointment with the attorney so it’s not You appearing to be calling the shots but everyone coming together on what works for everyone, protects dad’s assets and keeps peace in the family.
When sis is no longer to provide the care, perhaps needs care herself since she is disabled, then she needs to split living expenses with dad so he can continue to pay providers for a longer time. She also needs to look to her own future. I’m suspecting that a position as a paid caretaker might disrupt her disability income. When all the details are brought forward, a solution will hopefully be easier to negotiate.

This is not a criticism, just curious about it and looking to fill out the situation a bit...

But, why does this bother you?

My parents helped out all their adult children financially- at one point or another.

This included buying one brothers two boys cars - used but still nice - when they got their licenses and sending the other brother, his wife and son on a two week European vacation.

Still - one brother was always trying to keep track of who was given what. Not that my parents made a show of it. They actually tried their best to keep things even and somewhat private.

I always thought of it as none of my business. It was my parents money to do with it as they wished - and while they certainly weren’t wealthy, they were in no danger of running out of money or risking living comfortably in their “golden years”.
They had pensions, long term care insurance and income paying investments.

What bothers you about your father’s generosity towards your sister?

I do not see where she caregives. Looks like Dad supports her and her money gets spent on herself. Mention this to Dad, she is being paid. If anything, she should be paying him to live there.

I also agree with Florida, if he chooses to pay her, then tell him if he needs anything, she is the go to person. It always surprises me how people think.

If dad is competent, up to him.  But I would tell him that unless appropriate and documented correctly, it may result in him not being eligible for Medicaid down the road.   I would also tell him, that you see it is a gift, and he can give her all he wants, but when the time comes that he needs help, he should look to her, not you.