in general boxers seem to be very accepting of mma/muay thai as sports. however if you walk into a BOXING gym claiming one to be better they will be looking to put you in your place. if you walk into there humble and willing to learn, you should have no problem.
i wear sneakers/running shoes when training on the bag and wrestling shoes for matches and sparring.
Why don't you ask them about what to wear and what to expect? Didn't you check this place out?
Most boxing gyms, they are out to kill you.
You hit the bag for 1 month and then you go into the ring and fight to kill. If you are not good, you are someone's training partner and you are going to get hit.
Are you prepared for this?
This is not like a MMA gym or BJJ gym doing sparring where no one wants to hurt you.
Wrestling shoes should be fine.
I don't understand something, if you think you are a good enough boxer to join a boxing gym, why don't you have your own boxing gloves?
Nothing wrong with working on your boxing skills at a BJJ gym that does boxing or a MMA gym.
Until you've been training for a decent amount of time and picked up a good basic level of skill then no-one is going to be "out to kill you". Even in a sparring match, which can be painful, its almost never all out, full power, unless you're tuning up for an upcoming fight.
Turn up, be polite, be respectful, train hard, enjoy. Trainers are fine, they will provide gloves until you buy your own (they will probably stink though).
When you step into a boxing gym, shut your mouth about any previous martial arts training. News travels fast around the gym and guys will be out to check your chin.
Be careful of the kind of gym you join as well. I was training at a gym where most of the guys were on the amateur / pro trek and I was just a recreational boxer. Plus, I was about 33 when I started training.
The skill sets between them and myself was like night and day. Every time I stepped into the ring I was outclassed and pretty much got my butt kicked. I learned a lot about boxing and myself though, but this approach is probably not what the wisdom of King Solomon would advocate.
Also, be wary of some trainers as they are looking to pimp you - I have heard some trainers at the gym where try to get some not-so-good boxers (like myself) go amateur and then pro. The trainers usually stressed how much heart we had. Heart is important, but you need more than that to stay off the canvas.