how much of an obligation is required by law to accommodate someone like this example (brain injury causing impulse-control issues) if that person's behavior has a negative effect on the harmony of the club?
Legally, your obligation is the same as it is to any other disability. If accommodating it will endanger the club's survival, you don't have to, but you could be called upon to evidence this if challenged (which can be tricky). It's a lot easier to exclude the physically disabled, because if they can't get in, they can't get in. When you have someone with a behavioural condition (and I've known a few), then not accommodating them will mean effecting a ban, which immediately creates a conflict likely to go in bad directions.
Thankfully, most clubs absorb this sort of issue organically. People simply decline to play those with whom they don't get on. Theoretically, a club could be held liable if they were seen to encourage a culture of exclusion, but in practice it can't be held responsible for the private preferences of its members.
Our hobby does tend to appeal to those on the autistic spectrum, and those who are higher up can be hard work. But in my experience, there tend to be club members who will tolerate the behaviour of such comrades (it's good practice for dealing with the douches who don't have the excuse of a mental illness or behavioural condition). Clubs may like to offer free gaming for example to those who help others with access issues - physical or mental - to participate: by painting their minis, building adapted tables or terrain, or just by agreeing to throw down with them.
It's all part of what makes a club into a community.
