It's not usually in a large gym, but if your place is dominated by private education, it's hard to say whether they deliberately create that kind of discriminatory atmosphere.
After all, according to your description, this small gym may be jointly invested by these private teachers, or they may be the boss, so they may prefer customers to spend more money. It is possible to put pressure on you to spend money, but it is not 100%.
Therefore, it is mainly about people. If you are professional, you shouldn't do such a thing.
Some things may be that you think too much and give yourself pressure. If they are found to have discriminatory behavior or words, change the gym. If not, don't think too much and don't put pressure on yourself.