Of course based on bacteria/virus mutations
Let’s say I get a full battery of modern vaccinations including smallpox for my time travel adventure in the past. How far into the past could I go and still reasonably expect to be individually (since no herd) immune? And I understand it may be different times for different illnesses.
Interesting question! I don’t know what would be the last (non-smallpox) lethal disease that’s been eradicated or replaced with a different strain. The flu of 1918 is a strong candidate, though. It’s possible that current-era flu immunizations would/do give one immunity, but I don’t think we know that for sure (I seem to recall there’s a lot of dissent about whether those particular buggies mutated into something far less lethal, but basically stayed around as flu strains we’ve still got, or if instead we’d be in deep shit if someone dug up a preserved corpse from WW I and unleashed it on us anew).
Then there’s the non-virus pathogens to consider. You’d be in a hell of a bad situation if you encountered the bubonic plague, unless, in addition to vaccinations, you get to bring back with you some antibiotics to shoot yourself up with as need be.
So to add to the scenario, would I be safe from the Spanish Flu if I traveled back before 1918? AIDS before the 1960s?
Presumably yes, as it’s believed neither of those specific diseases existed before those dates.
About 1967 as primary school aged child I picked up a dose of chicken pox which was doing the rounds of the district.
No biggie.
In 1987 I went on a business trip to the US and came back rather run down and was clever enough to pick up the variant of chicken pox which was circulating in Sydney at that time.
You have a significantly larger surface area to blister in your late 20s.
I’ve never had shingles.
(Not a doctor so take this with a grain of salt. Three times a day. With meals)
You’d be safe from AIDS because before it first jumped from animal hosts there were no other comparable diseases doing the rounds among humans (as far as I know)
As for influenza, you might be pretty safe from Spanish Flu before early 1918, but there were other influenzas (and possibly coronaviruses) circulating around which it eventually displaced. While they were endemic and had been since the 1890s pandemic, your own immunity to them would likely be negligible, so it would hit you hard, possibly fatally hard.
Current flu vaccine is based on what is known and expected to be circulating at the time of your vaccination. If it accounted for unknown variants then it would fit the bill as a more general cure for the flu.
I don’t know what the story is with other diseases like the whooping cough, tetanus or the marthambles, and whether they are likely to respond to the same vaccine as modern strains.,
Which is why we have to get it renewed every year. I am booked in for mine in a couple of weeks.
Of course, vaccines also aren’t all-or-nothing. If you’re exposed to a flu virus, and you’ve had a vaccine tailored to that exact variant of the flu within the past few months, then you’ll be almost completely immune to that virus. If you had exactly the right vaccine, but a few years ago, or a recent vaccine for a different flu strain, you’ll probably get sick, but not nearly as badly as if you hadn’t been vaccinated. And if you’ve ever had any exposure to any flu variant (by vaccine or by the disease), you’ll probably be better off than someone who’s never had any flu exposure at all.
I would expect that the same would be true for time-travelers. Even if your smallpox vaccine isn’t exactly the same as the smallpox going around in the 10th century, it’ll still provide you with a significant (though maybe not total) amount of protection. And remember that even exposure to a virus as different as cowpox was enough to make a lifesaving difference. I expect that Modern Smallpox and Old Smallpox are at least as similar to each other as either is to cowpox.
Yes, but are they mutually intelligible? 
There’s now some speculation that the 1890 pandemic was a coronovirus.
It changed the course of history in Britain, by carrying off Prince Albert Victor, who was second in line to the throne, after his father, who became Edward VII. Albert Victor was thought to be … well, not smart. He was replaced as heir by his brother George, who became George V.
There was also variola major, which had an extremely high fatality rate, and variola minor, with a fatality rate in the single digits, but they were caused by the same virus, probably different strains.
p.s. The weirdest thing I’ve heard of a vaccine being developed for? Acne. I kid you not; in the 1930s, someone cooked up Elixir of Zit Bacteria and injected teenagers with it. It worked about as well as one might expect.