I've been running Blue Bullets in 9mm for a while and love them so I just picked up some 180gr for loading 10mm. They don't list the hardness of the bullets nor any suggested velocities. Anyone have an idea? Would it be safe running these up to 1250-1300 ft/s?

When you say blue bullets I suppose you mean Polymer Powdered Paint coated bullets which is baked to cure the paint.
These have held up well and many companies and handloaders are using the process.  It seals the bore well and slides through without leading providing they don't exceed the alloy's strength as the take to rifling.

We have seen some people run their's in rifles at some extreme speeds with no issues.  YMMV not knowing the BHN of the alloy, but you are likely to be OK out to 1150 and possibly 1200 fps.

I will say I am shooting my own cast bullets properly sized and quality lube in excess of 1200 in some cartridges like 9x25Dillon @ 1700 + fps.

Shadow, I think the OP is talking specifically about http://www.thebluebullets.com/

I've used their 125s in 9 and 200s in the 10, they perform well.

I haven't tested hardness, but would suggest their alloy is softer than comparable bullets (BBI, Missouri, Badman) - Just my impression.

I doubt you'd have any issue running up around 1,300.

By their photos on the website, they appear to be swaged. That usually means very soft, nearly pure lead (most plated bullets are swaged). The bullets shouldn't have a speed limit in any 10mm load, but there may be concern for the "polymer coating". I dunno. It's probably free to ask. I'd just shoot 'em, if it were me.

Sorry, they are from thebluebullets.com. I did ask them and they said their bullets can be run up pretty high but didn't rest on a particular velocity. I was just wondering what folks here had experienced.

I tried to run Missouri Bullet Company's hardcast in 180 grain but they have been the source of all my chamber in issues in my aftermarket glock barrel. Bluebullets seem to fit with no issues.

Have you slugged the bore of the gun?

As long as the bullets measure at least .0005" and ideally .001" over measured groove diameter, you can run them at 10mm velocities with fine results.