fellow - what-?
How do you call a person who you go to the gym with? You call people who you travel with 'felllow travellers', who you study with - 'fellow students', you work with - 'fellow workers'. How do you call people who go to the gym with you - 'fellow - who-?'

Question

fellow - what-?
How do you call a person who you go to the gym with? You call people who you travel with  'felllow travellers', who you study with - 'fellow students', you work with - 'fellow workers'. How do you call people who go to the gym with you - 'fellow - who-?'

Answer

You could use the same pattern "fellow gym goers", but for each there are usually more specific words:
fellow students - classmates
fellow workers - colleagues
fellow gym goers:  I do not think there is a formal word for this relationship, however you often hear people say "my gym buddy" or "my workout buddy" to show that they are your partner in that activity.

Answer

Your expressions with "fellow" are all excellent and natural.  They are just a bit more formal than Chad's suggestions.

Answer

Fellow gym members or fellow gym goers?