Customize scenario visibility for some entities

I am not sure how you can accomplish that with a BR. I would use Data Access Security to restrict the Entity and Scenario combination.

Data Access Security is your best bet.  You can set just those entities (all other entities to which this does not apply can remain "False" to True for "Use Cube Data Access".

Then on the cube(s) you would add a few slices something like below.  This is just an example so please test:

1. The first slice should have a filter that grants access to users to which this does not apply (something like second screen shot below) giving them read all to budget
2. The second slice should have a filter that grants access to users to which this does not apply (something like third screen shot below) giving them write all to budget
3. Then you will have a final slice that denies access to these entities to users who are not in the above two groups (last screen shot below)

First slice example:

Second slice example:

Third slice example:

If this applies to "Everyone" you may not need the first two slices and the one remaining slice can have access group "Everyone".  Native administrators bypass slice security so this would not apply to them since someone needs to view these entities.

Slice will work.  You just need to set up and test on these handful of entities.