This means no sales, no themed merchandise, no decorations. December 25 and most other day are treated just like any other day for all stores malls, restaurants, ect.
You’d still get non religious holiday events like mothers days, or independence days.
What whould change?
We’d get non religious holidays developing / being promoted to sell a bunch of shit. Some people classify halloween as a “religious holiday” because of its roots as All Saints Day eve, but it’s pretty clearly a nonreligious “dress-up / horror” holiday nowadays.
If there was no Christmas there would be some generic winter cosiness holiday (as xmas/ December actually is for most Western countries). I live in France and there’s loads of “Christmas” junk but it’s 99% non religious. Even compared to the UK, where some people complain about “Christmas loosing its roots”, it’s noticeable to me how few of the decorations or cards have any religious imagery (even pretty neutral things like stars or angels). There loads of snow and winter animals, no wise men/shepherds, let alone ‘baby jesus’. France is officially opposed to religious holidays because they’re a “secular state” but they keep a winter and spring public holdiays that are at the same time as Christmas and around Easter. But other public days off are just other non religious events (national holidays like Bastille day, workers rights on may day, etc.)
And in seasons like summer that didn’t have big religious holidays (or not popular ones anyway), there’s loads of secular sources of themes / merchandising. The Olympics and World Cup (or whatever sports your country is into) always end up filling the supermarkets with loads of cheap junk and create a shared topic to “being people together”.
Another French holiday is the midsummer “fête de musique” which was created by the government decades ago to replace the dangerous (notionally Christian but clearly pagan) “fête de Saint Jean” where people built big bonfires and young men tried to jump over them (leading to lots of injuries!). Now all cities and towns and even small villages will organise some concerts or live music evenings.
Tldr : if companies weren’t promoting religious holidays, they’d just find other holidays to sell stuff.
Now what happens to a religion that is, for the most part, now separated from capitalism?
Really depends on the religion. There are some religions that aren’t organized at all, and are fully self practiced. They don’t require things to be sold.
The religion of capitalism is a different beast though. I would say that people need things to celebrate in life though, or they tend to get very hostile. It seems to me that the more communal an event is the better the effect is on society, as people can set aside a lot of grievances for the festivities.