Old School is becoming something of a meaningless term in gaming. It seems to mostly have a nebulous meaning roughly equivalent to "whatever feels most like the games I played when I was younger."
I'll start by agreeing that it's a mistake to equate the old school crowd with any form of bigotry. Some might feel that way, but it's a bad generalization to try to tie a preference to an older or newer ruleset to a position in the culture wars. Ernie Gygax made that mistake earlier this year, and it would be just as much of a mistake to take the opposite position, that people want to use older rules or retroclones because they want to oppress women or minorities.
No, the old school position is mostly motivated by issues from within the hobby itself. Some of it predates WotC; there are players who stopped active buying stuff because they didn't like how Gary got forced out of TSR or how TSR caved to the Satanic Panic and so on. Some people didn't like how the rules were being changed in late 1e, and since 2e generally followed those trends, they tend to dislike newer stuff. They were already lost by the time WotC bought TSR.
And some people prefer to stick with a ruleset rather than change things. Unfortunately, 3.0, 3.5, 4e, and/or 5e are part of the problem here, there are some players who feel a certain amount of edition fatigue over all the changes and are less motivated to switch to a new edition. This is especially true of players who have dealt with issues they had with older rules by houseruling. Or in other cases they found a retroclone that was compatible with their preferences. In addition, I've come to the opinion that the old classic D&D game is a pretty solid set of rules in its own right. It's not bogged down with 1e's language and Byzantine complexity, nor is it too burdened by the complexity of options offered by later games. It's a little too simple for my taste, but I can definitely see its appeal.
One particular issue is how WotC does surveys WRT age groups. WotC tends to focus on high school and college aged players in their surveys. Some older gamers don't like that and feel they're being left out, and that contributes to some of the animus they feel towards WotC.
In addition, there's some of TSR's bad business policies combined with William's well documented contempt for gamers. As a result, the old distrust of TSR's suits has spilled over into a distrust of supposed suits who work for WotC and/or Hasbro.
Some of the people who feel alienated by WotC/Hasbro have some fairly irrational views, but I think WotC should simply ignore them. They're not going to come around, and they have more noise than actual influence. Just keep the classic stuff available on the DMs Guild, and they'll buy that stuff anyway no matter how much they hate anything after 2e.
Anyway, this tweet wasn't necessary IMO (is there any such thing as a necessary tweet? Well besides advertising.) Reading it, some people are going to read a confrontational tone in it. If you read it a certain way, it can come off as "I've been playing just as long as you, so I'm old school too and so is my work, nyah nyah." I suspect some of the old school crowd will get annoyed over it, they're not going to be convinced by it. I don't personally feel that way, but I know some people are going to think this.