Yeah, antivaxxers are annoying. But there's also a large number of people who weren't vaccinated for all kinds of reasons that just never cared.
Most pharmacy chains have it in stock and offer it to walk-in patients. If you are sure you've never had any MMR vaccine at all, they may recommend two shots, separated in time.
I know in Germany the recommendation for the MMR vaccine is to just give it to all adults that aren't sure if they got it as a child (for all adults born after 1970, because they assume all born before almost certainly had the disease).
Subsequent shots don't decrease one's immunity, but they can still produce the same side effects as the initial vaccination, which are usually mild. For example, I experienced mild arm soreness for four to five days, which is the most common MMR side effect.
Feel free to ask your own doctor or pharmacist! :-)
Another important childhood vaccine that would be covered in the 85% global statistic is the different variants of DTP.