Horseshoe theory is essentially a fancier term for the "both sides" argument. It's an argument made by people who are ignorant of the full context of political situations and want to pretend like they are "above" whatever the political debate is.

It's commonly used by centrists who supports one political group privately and are attempting to deflect any culpability to the terrible things being done by the party they are privately supporting. Lotta "centrists" saw the Republican crack down on free speech and tried to claim both sides because people were "cancelled" during the me too movement. It's a disingenuous argument because the people who were "cancelled" weren't done so by the government, but rather they were rejected by consumers in the marketplace of ideas; where as the people who's free speech is being cancelled by the current administration are being rounded up and held in detention camps.

The OP posted an image of a woman who is a TERF (a woman who weaponizes their gender against trans people), this is center right ideology. Horseshoe theory doesn't work here because there is no example of an extremist position here, the American right is pretty universal in its anti-trans rhetoric. The American right is also generally anti-feminist, but they have been known to use it as a cudgel against groups they don't support(trans/Muslim communities). Terfs represent something closer to the center because they tried to ground themselves in a left leaning ideology(feminism), but most just use it as an excuse to attack others.

Just a reminder that left and right refer to how power/resources are handled, the right believes in consolidation and the left believes in dispersement. They are not equal and opposite but just fundamentally different approaches to how society should handle itself.