TL;DR
Probably yes, natural uranium (NU) is usable in weapons in "young" [note 1] solar systems. (not weapons-grade, but weapons-usable)
Probably yes, terrorists would have a much easier time creating (crude) nuclear weapons. Whether not needing enrichment would hinder or help civilizations prosper and survive is uncertain since there are both problems (terrorism, nuclear proliferation) and benefits (cheaper nuclear energy).
NU enrichment levels
2 billion years ago NU was enriched enough to sustain a nuclear chain reaction (Oklo cave was probably a natural nuclear reactor)
4.5 billion years ago natural uranium was already enriched enough (~23%) to be used in weapons without the need for further enrichment (although enrichment would still be beneficial).
Using the code at the bottom we get the following results:
2 billion years ago natural uranium was 3.7% enriched.
4 billion years ago, 16.7%.
5 billion years ago (about the age of our solar system) 31%.
6 billion years ago, 51%.
On the other hand we are not quite certain how life on earth formed and perhaps there is a time threshold on how fast life can form in a freshly created solar system, eg. requiring at least 1 billion years for multicellular organisms to form etc.
By going into an even earlier period higher enrichments are possible but probably unlikely, since $\ ^{235}U$ and $\ ^{238}U$ are created through the r-process and their abundance when created is probably not that different (about 1.5 $\frac{\ ^{235}U}{\ ^{238}U}$ = 60% enrichement in supernovas).
By comparison U used in nuclear reactors is about 3-5%, meaning that both state-owned nuclear weapons and nuclear reactors are widespread in planets that are "young".
So, yes. Natural uranium was weapons-usable and perhaps is weapons-usable in other "young" solar systems as we speak. Is the relative age the only way to have enriched NU? If uranium can be transfered to a planet by asteroids or comets just like water on Earth, then "young" age is not the only way to have planets with enriched NU.
Nuclear terrorism
When it comes to terrorists (today):
once they have [the nuclear material], 80% or more of the way [to a crude nuclear bomb]
Also,
once enriched from 0.7% U-235 to 4.5%, ~3/4 of the work of going to 90% U-235 is done
having a stock of LEU could allow a country to enrich to HEU more quickly, or with a smaller, easier-to-hide facility
Meaning that the greatest obstacle is U enrichment. With that out of the way, everything becomes much easier! Both nuclear proliferation and terrorism would be increased.
Perhaps that's an extra great filter for civilizations on young solar systems. Once they've solved the terrorism/wars issue naturally enriched U is a blessing instead. Perhaps one day we'll be able to detect nuclear detonations from distant solar systems and we'll find out.
Note 1: "young" compared to when the nearby supernova exploded creating its elements (including the U).
Note 2: I answered my own question so that you can check it. If you find any mistakes, let me know.
Python code used for the above results:
SECONDS_PER_YEAR = 365*24*60*60
BILLION_YEARS_TO_SECONDS = SECONDS_PER_YEAR * 1e9
U235_halflife = 7.04e8 * SECONDS_PER_YEAR # http://www.nndc.bnl.gov/nudat2/reCenter.jsp?z=92&n=143
U238_halflife = 4.468e9 * SECONDS_PER_YEAR # http://www.nndc.bnl.gov/nudat2/reCenter.jsp?z=92&n=146
U235_TO_U238_RATIO = 0.720 / 100 # https://physics.nist.gov/PhysRefData/Handbook/Tables/uraniumtable1.htm
# --------------------------------
# CHANGE THIS VALUE:
bil_years = 5
#
# --------------------------------
u235_halflives = BILLION_YEARS_TO_SECONDS * bil_years / U235_halflife
u238_halflives = BILLION_YEARS_TO_SECONDS * bil_years / U238_halflife
# If there are 0.0072 parts of U-235 for every 1 part of natural U
# then we calculate the "initial" quantity (a few billion years ago)
quantity_235 = U235_TO_U238_RATIO * 2 ** u235_halflives
quantity_238 = (1-U235_TO_U238_RATIO) * 2 ** u238_halflives
ratio_235_238 = quantity_235 / quantity_238
print('Billion years: {}\n'.format(bil_years))
print('235 quantity: {:.3}'.format(quantity_235))
print('238 quantity: {:.3}'.format(quantity_238))
print('ratio_235_238: {:.3}'.format(ratio_235_238))
enrichment = quantity_235 / (quantity_235 + quantity_238)
print('enrichment: {:.1%}'.format(enrichment))