BFP stands for back focal plane. Most UIS2 objectives have a BFP of either -19.1 or -25. There are several exceptions and they require special condenser prisms, usually. I will ignore those. Olympus' objective selector will show this if you are interested.

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- Normal position appears darker but background is uneven
- Colour variance
- Intensity variance
- With the BFP1 latch engaged, the image can be made very dark by engaging the translation knob. The normal position will always showcase a weird bright spot.
- Only applicable to this specific objective/prism combination. Others may see a more/less prone effect.
Boosted...

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Here is an animated illustration for the valve. The BFP1 slider ensures that the extraordinary and ordinary waves split by the condenser prism gets combined correctly. It lowers the prism by around 6mm.
Is there a difference? Clearly, yes.
Does it matter? Probably not, background can be replaced/cleaned. The minute intensity difference/unevenness is hardly noticeable.
Does it depend on the objective? Likely, the effect could be more or less prone, but this is just a guess.
Enjoy.