It'd be sort of like airport security letting through someone with a blowgun because they're trained to look for modern guns.
Ideally we'd quickly gain immunity to the parasite or there would sell be some subset of humans with a resistance that they could spread to the rest of the population, but that's not always a given.
Depending on how far back you go, today's planetary environment is a very different place - in terms of chemical food, predatory tactics, biochemical efficiency, atmosphere, etc. Having to compete against organisms that are efficiently adapted in our current environment will almost certainly be immediately lethal for these revived organisms.
That is not to say that a virulent plague would not be a bad thing for a lot of individuals, if not the human species - but it'd be pretty challenging to even design worse than already exist out there - HIV, ebola, marburg or smallpox.
Something equivalent in virality and lethality to smallpox could be catastrophic if you consider the geopolitical consequences as well as the initial biological impact.
A nonlinear system, like an epidemic, can have phase changes. Most epidemics don't make it very far, but we should still be nervous about that one which crosses the manifold into pandemic.
In evolution, a population gaining immunity means that all individuals without the immunity die out before spreading their genes. Yeah, still not the ideal scenario...
When the white man arrived in South America and in Australia the diseases they carried devastated native populations.
Even though in the case of Australia they had been separated for over 50,000 years.
HIV came from chimpanzees - evolutionary distance 5 Million years.New influenza strains regularly come from chickens and pigs.
So what you are saying is complete nonsense.
Famous last words
It's like the concerns about high-energy collisions doing something terrible like forming micro-blackholes and eating the Earth. If that was a danger, it would be something Nature would already be doing and we'd be able to see it.
The ability to "infect" something is not a natural property that all bacteria have. It is something that has to evolve. A bacteria popping out of cold storage from half a million years ago precisely adapted to infect a modern animal would be every bit as weird as seeing a bacteria pop out of that same cold storage that was precisely evolved to live on Mars, or live on vast quantities of plastic, or otherwise adapted to conditions it couldn't possible have witnessed during its previous life.
It isn't absolutely, mathematically impossible. But it's not much worth worrying about. It's a science fiction storyline, not something that happens.
Now, if there were humans in such cold storage, I would be somewhat more careful. But so far in those cases where that has occurred we still haven't been wiped out. I haven't even heard of anyone pinning so much as a cold virus on pulling a cadaver out of a glacier. Links welcome if anybody does have such a story.
And the Black Plague did happen to come by less than a century after the end of the warm period...
I don't think we need to hypothesize that the Black Plague was some sort of bacterial refugee from the past; I've never heard anyone express any confusion about where it could possibly have come from, so it seems like a solution to a non-problem.
An asteroid can impact with the earth... Oh wait, that's happened already. Luckily, we haven't had such a collision large enough to kill us all, yet.
A plague could kill many people... Oh wait, that's happened already. Luckily, we haven't had a plague with enough virality and lethality to kill us all, yet.