Let's say for the sake of argument that time travel is possible and just an engineering issue. It doesn't matter whether technology will allow it tomorrow or one thousand years from now. Just imagine time travel becomes a scientific fact. Many aspects of society would change. Not even pseudoscience would be safe.
As an example take astrology. From the invention of the wheel to the invention of the selfie stick astrology has remained relatively unabated in the face of scientific progress. It seems a reasonable assumption to believe that astrology will still exist when society begins to manipulate time at will.
Time travel technology does however do something that no other technology has or will probably do. It poses the question of how to chart the horoscope of someone's day before the person is even born. If a person born on January 8, 2117 goes back and lives life in late 2016 then it's like their entire chart is moved almost the whole precession of the Earth's axis. But much like the Y2K bug would have set the date back to the year 1900 you can't say it makes practical sense to treat the time travel's horoscope like they are living in the 281st century when it's 2016.
I've read four books on astrology but I can't quite figure out how astrologers would deal with time travel. For lack of a name I will call such a method chronoscartography. Astrocartography is locational astrology but instead of using a chart to determine if New Zealand would be a good place for a person to live astrologically; chronoscartography would help determine whether the time period traveled to would be astrologically sound.
Normally the only planets that retrograde in an astrology chart are Mercury, Venus and Mars. But if you travel back to before you are born don't all the planets (even Pluto which astrologers still consider a planet) retrograde?
This is the type of idea that keeps me up at night.
If you meditate, you could travel, only you need to get the 7° dimension, not to easy.
The birth-chart (aka radix-chart) of that person remains the same. A 90 year old still wears the particular "cosmic fingerprint" acquired at birth.
For predictions, astrologers use the horoscope of any particular time in the future called transit-charts, superimpose it onto a radix-chart and study the aspects these two charts form. I don't see a reason why the same principle shouldn't be applied to a date 100 years before a person was actually born. It would still be a prediction would it not, for these 100 years would still lie ahead of the time traveller? The transiting points would certainly form different aspects of his/her radix-chart. It would be interesting to see how an individual would experience this, for it would shatter the natural cycles he/she was living before.
But what about space travel? A human who is born, let's say, on Mars? There would be no Mars in that horoscope, but an earth. What would that mean for that human? Not to mention a birth taking place outside our solar system. Geo- and heliocentric astrology would definitely be rendered unusable.
Last, but not least, seen from our geocentric perspective, every planet has its retrograde phases.
As per natal chart, you can always use heliocentric system, where Sun is in middle of the chart (so you don't see it as a glyph) and Earth and Moon are together. Though, I haven't seen many astrologers using this system ...