What's the exposure level for an exposed Halogen capsule?
It seems like it would not be a lot because it is a Blackbody Radiator, and it would get very low once it gets to Blue or UVA. Is this true?

They have some UV. Definitely not a health concern, not much of a plastic degradation concern unless it is in the bright spot of the light, but it is sufficient to discolor things exposed to it for years

Then why do they tell you to always under any circumstances keep the filter on?

Lamp explosions

Lamp explosions

Oh, right.

Halogen UV radiation occurs from Halogen lights that are running overvoltage-when people run them at higher voltages to get a higher kelvin rating,cooler light color from the Halogen lamps.Bulb explosions are the greater risk here-so the Halogen bulbs have to be run in an enclosed fixture.Warnings I find in lamp catalogs.

I've heard when I was younger (During the period when indirect ceiling halogen fixtures on dimmers, were common), that the UV of halogen lamps can be dangerous. This was the reason why on many Osram and other manufacturers halogen lamps, there were a statement of "No UV" or "UV Free".

The lighting standards impose a maximum limit of the UV content, the original motivation is to make sure mainly the discharge lamps (with the UV content being high and includes high energy bands) have proper filtering. And as usual, the limit was set so low, to be sure it does not poses any possible harm. The same approach for any such unwanted hazard...

Then the fact is, the filament lamps, when operated at temperatures above 2800K or so do emit UV in quantities exceeding that limit.
Most likely the regular incandescents would exceed that limit as well, if the UV wouldn't be absorbed by the glass bulb. The problem with halogens is, the high operating temperatures require to use a glass mixes (mainly the pure quartz, used on the hottest running types), that in their basic form pass way more of the UV than the soda-lime of the classic incandescents. So unlike the classic incandescents, the halogen lamps did exceed those safety limits for the UV, so in the early days required external filter to fulfill the standard requirements.
After some time the halogen makers came up with a doping into the bulb material, which makes the bulb opaque to thee UV, while maintaining the required temperature robustness. These designs then did meet the UV limits, hence the "NO UV" or "UV-free" lamps were born.

Even when the UV power generated by incandescents is not that high, I wouldn't underestimate it's danger mainly with long term exposure in close distance from the lamps (desk/reading lamps,...).

Is there enough UV to use Halogens as a crude germicidal lamp?
Is there enough UV to cause bad eye damage?
These lamp standards seem silly.

Is there enough UV to use Halogens as a crude germicidal lamp?

No at all. For that you need UV-C with guaranteed output power (you have to be sure it really works)

Is there enough UV to cause bad eye damage?

Depends on the exact use. With some uses no, with some uses yes. Of course, the danger is not of the short term one, but longer term exposure with an unfortunate setup may become too much and cause problems.
It depends on the illumination level in that area and how the eyes respond to it - if the iris contracts, so reduces the overall internal eye exposure, how the illumination is aimed,...

These lamp standards seem silly.

Say that to someone who got his sight permanently damaged by an excessive UV exposure...
The border, where the UV output becomes problematic is indeed very fuzzy, as it depends on huge amount of the other factors. But as those are practically not possible to control with a general purpose lamps, it is not that bad practice to set the limit low enough. The UV filtering cost nearly nothing, mainly compare to the damage the uncontrolled exposure may cause and it is still way cheaper than would be an attempt to really control the other factors influencing the possible danger.

Yes, there are lamps that intentionally emit UV beyond the standard limits, but these are rather explicitly designated for the given special use, where the other conditions are supposed to be under control (e.g. exact spectrum composition and exposure time with sun tanning beds or so).