Is there a word for enjoying something, but disliking the fact that other people enjoy it or disliking the way they enjoy it?

Solution 1:

People often express their pride and/or current frustration at having enjoyed something before it became popular by saying that they liked it before it was cool.

There are many variations on this phrase. Here are some I pulled from a corpus:

1. I supported Bernie Sanders before it was cool
2. I used to eat Peruvian food before it was cool
3. I was tea party before it was cool
4. I liked Alexander Hamilton before it was cool
5. He was advocating mindfulness before it was cool.
6. the fans that loved this team before it was cool
7. Martin Castrogiovanni had a beard before it was cool
8. Roman Philosopher Seneca worried about information overload nearly 2, 000 years before it was cool.
9. the age group that supported Barack Obama before it was cool

When people say that they liked something before it was cool, it doesn't necessarily mean that they no longer like that thing. They may just be bragging about being an early adopter.

That said, many people do use the phrase with such intonation as to convey the fact that they no longer like the thing, or that they still like it but are disappointed that it's become so popular. Here is an article about this use of the phrase.

Another variant of the phrase is before it was mainstream, where mainstream means "popular." Here are some examples:

10. I liked it before it was mainstream.
11. I was taking selfies before it was mainstream.

Sometimes people will even claim that something has become too mainstream, as in

12. This song used to be good, but now it's too mainstream. (cf. here)

Other variants include

• I liked it before it was popular.
• I liked it before it blew up.

If you're looking for an adjective which describes a person who becomes disappointed when something they like becomes popular, you might consider protective or jealous in the sense of:

fiercely protective or vigilant of one's rights or possessions.

More broadly, one can be jealous (that is, fiercely protective) with respect to one's favorite bands and TV shows.

Solution 2:

The word hipster comes to mind ;)

While hipster embodies richer character than just shirking away from mainstream stuff, that particular character seems to be the strongest evidence of being one.

This article highlights that aspect:

http://bostinno.streetwise.co/2012/01/17/the-scientific-explanation-of-why-youre-a-hipster-hate-mainstream-music-from-harvard-of-course/

Solution 3:

You like things when they are still cool.

Some more ideas in this Stanford article The Tipping Point of "Cool"

Research shows that popular products can quickly lose their cache if they become favored by the masses. [...] other words, as soon as chic goes mainstream, [...]. Cool had suddenly become uncool, and when too many others liked an item it was no longer a good marker of identity  a cool item became passé when it was perceived that an uncool group also favored it [...] stay ahead of the cool-passé pendulum swing. 

I recommend reading whole article.