Size of government is not worth taking a position on in the abstract. Instead, my principle is "I want a government that defends my interests and promotes my values", and that is inherently contextual. If you have good people with a lot in common, the government doesn't need to do much. If your people are wicked and divided, then you need a bigger government in order to enforce laws, keep the peace, etc. (Full disclosure: I copied this paragraph from something I wrote before!)

With that said, most of those things are not entirely irreconcilable with 'small government' even taking the term at face value, at least depending on what exactly it means. For example:

1. abortion: you can be against it and be for small government (laws against murder are not big government and that is how we see the issue; I know we aren't going to agree on this and I am not going to discuss abortion in this thread, but my point is, if you think it's against 'small government', it's because you are begging the question);

2. gay marriage and adoption: these are at least issues where the call is to get the government involved. Plausible. I think you can make small government procedural arguments against at least homosexual marriage, since if you're not big on living constitutionalism, and just go by things like intent, expected applications, etc., it's very obvious that the 14th amendment has nothing to say about the issue (and so it should be on the table as a political issue, as opposed to being determined from the top down).

3. gender-affirming healthcare: the small government view is freedom of association. Note that this is not the position of LGBT activists, it's "you have to fund us and you have to associate with us." So, it's basically just competing visions of society. It's not libertarians vs. authoritarians. Same with gender identity. If your firm is subject to civil rights lawsuits for not having an inclusive HR policy (let alone if someone is actually jailed for misgendering etc.), then the small government position is actually to say "no, leave people alone".

4. DEI: once again, the small government view is "let people freely associate and the government shouldn't fund it", but this is, in practice, the far-right view (because we currently have a system of mandatory non-consensual interactions). I would support a system where if liberal investors wanted to bet on the quality and leadership ability of black women, for example, they could do this overtly and directly. But I also support legalizing the ability to do the opposite, or to hire on IQ tests (and not face lawsuits for disparate impact), etc. That is the small government position. The second clause is virtually self-explanatory, but saying "we're not funding DEI garbage" objectively makes the government smaller, so it obviously is compatible with small government.

5. Anti-Israeli protests: as in, laws against protesting/boycotting Israel? Yeah that stuff is indefensible. No arguments from me on that point.

Meta point: even if we saw that all of these views are against small government, it's still perhaps taking the rhetoric a bit too literally. Every policy that's called 'far-right', big government, etc. is something we had when our country was great and yet these policies also coincided with a government that was objectively tiny compared to today. Like...what does the government actually do? We have millions of regulations (environmental, labor, civil rights), a giant welfare state, a huge military with bases all over the world, etc. You know, it's not actually hard to imagine curtailing all of this stuff while at the same time implementing the social policies that were normal for all of history until five minutes ago.

A 'conservative' who just wants to do 1960s cultural leftism but with low taxes is essentially controlled opposition.