OP, I think it is a really good idea to trade up the bicycle for Christmas if he still is into mountain biking.
I really understand the pressure of labels and we are very grateful that there is a school uniform policy. It can be hard for the children.
We are very open that we have less money than their friends’ parents - and it is obvious on play dates where their friends have big houses with gardens (and sometimes staff) and we have a small flat. Our children accept that and do not ask for many things (well, PlayStation- over my dead body, phones - only in secondary school).
We do (as per my previous post) try to get some select label items on eBay.
For any kind of sports or music, we put a strong emphasis on skill. I repeatedly tell our children that the most stupid thing in the world is somebody with expensive gear and no skill. In music, you need a decent instrument about grade 4/5 and a good instrument about grade 6/7. Our children have decent/good instruments as they play at reasonable levels (at least grade 3 in year 3, at lest grade 7 in year 7 etc) but no child with less skill (which are most in their schools) gets away with teasing them. One boy tried with our son, the answer from DS was “cool instrument, too bad about your playing”.
I think it is the same with all sports as well. Tease DS about his football trainers (his friends wouldn’t anyway) and he would nutmeg them multiple times next session. Tease DD about her netball trainers and that person wouldn’t see the ball next session.
It seems to be the same for mountain biking. If your DS really loves it and becomes really good, his friends won’t be able to tease him, he would easily make them look very stupid. As he seem to be a beginner, he shouldn’t have the gear in my opinion. If he sticks with it and loves it, he can slowly upgrade.
It is interesting with the “labels as armours” theory. I think there is a lot to it. We use “skills as armours” and that works as well or better.
I do put a lot of emphasis on manners as well. And on table manners. We see a lot of rich children who cannot use cutlery properly and who seem to spend a huge amount of time on screens. In my experience that is due to parents outsourcing a lot of the upbringing to non-qualified nannies. The nannies let the children do what they want after school and cannot be bothered to emphasise table manners, they only set the table with forks and spoons and don’t eat with the children whereas the parents eat separately. These children can have all labels in the world but are uncomfortable eating with non-familiar adults (DH and I) and sometimes try to copy our children when we have dinner. We try to make them comfortable but I feel really sorry for them.
Money cannot buy you manners or skills and this is what we are trying to teach our children. It does work for us.