Are TERFs and SWERFs "socially conservative"?

[Okay, maybe Mike Johnson is a competent parliamentarian.]

Of course not. It's not even clear to me that hostility towards the sex industry is itself the socially conservative position on the subject (noted #wokebae pro-brothel politician Matteo Salvini says hello), although hostility towards trans people definitely is.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

I think what's often missed is just how out there actual TERFs/SWERFs are even on issues that have nothing to do with trans people or sex work. They are not simply "feminists/otherwise non-socially conservative who don't like trans people/commercial sex." Some proposals I've unironically seen from actual TERFs/SWERFs include:

-A tax that only men are charged.
-A curfew that only applies to men.
-Eliminating presumption of innocence in rape cases.
-Banning urinals.

(OK that last one wouldn't have anywhere near as far reaching negative effects but seriously think of just how f[inks]ed in the head someone would have to be to consider that a cause worthy of attention.)

These still aren't "socially conservative" positions though except in the sense that the third one, as the poster above me says, could be framed as "tough on crime".

[Okay, maybe Mike Johnson is a competent parliamentarian.]

There's also a fringe undercurrent of lesbianism being fine/ in some cases preferred (eventually...there was a lot of lesbian and bi erasure early on)

Yes; see Shulamith "what do you mean this radical feminist house party doesn't have men at it to hook up with?!" Firestone, for instance.

but a very conservative take on male homosexuality being wrong as it includes sexual gratification and the expression of sexuality without women and is therefore misogynistic (long forgotten groups like Redstockings etc)

That's the natural conclusion of some of the crassest "penetrative sex is rape" or whatever takes, yeah; the more people involved in the sex act who are capable of penetration, the rape-er it is.

While fringe some of that does rear it's ugly head online (there's a great account on twitter about Gender Critical homophobia) in recent years. Especially around issues of surrogacy and adoption.

I know MRDA to me saying this, but I don't think surrogacy and same-sex adoption are really equivalent issues, even though homophobes often attack them as though they are. There are pretty straightforward "orthodox" feminist arguments against the former, even if one doesn't agree with those arguments, which there really are not against the latter.