For instance, there have been instances where legislation has been proposed that could limit or coerce free speech, such as through restrictions on dead naming and misgendering.
I'm not familiar with those proposed laws off the top of my head. BUT, on the other hand, when you're working at a job, your employer can compel certain speech, and if you won't comply, you can be fired. If you're talking about legislation that compels e.g. teachers to call students by the pronouns that they use, then I don't see a problem with that, because it's regulating teachers in their capacity as employees of the state, not in their individual capacity. If a teacher doesn't want to do that, then they are absolutely free to seek employment at a private institution that isn't funded by the state. (...Which will then compel their speech in other ways, and perhaps in much more restrictive ways.)
Your religion may compel you to evangelize. But if you evangelize while you are acting in your capacity as a state employee, then you are violating separation of church and state. So prohibiting that speech while you are acting a representative for the state doesn't not harm your individual rights in a significant way.
TRUE equality does not discriminate based on race or gender
Sure. But we still see discrimination now. We're not at a point where people are treated equally in places they live, schools they go to, career choices, policing, etc. Acting as though certain demographics don't need more support in certain areas than other demographics do isn't going to get us there either; it's just going to widen the gap. If society truly treated people equally now, then you'd see highly competitive schools with demographics that roughly mirrored the population as a whole (..which you do, because they have intentionally worked towards diversity and inclusion, rather than looking solely at "merit").
(ie, the shifting role of a father in a family, being replaced instead by "Big Brother")
Why would shifting the role of father be bad? I'm not saying that the father should be replaced by the state, but why is a traditional father role better than a father that's a nurturing home maker, and a mother that's the primary provider? Or two fathers? Or two mothers? Or a blended family with two fathers and two mothers? Men benefit in all of those cases, because they have more options that can suit who they believe themselves to be, rather than what society expects of them. Men get to choose their role, rather than having one assigned to them.
Yet, "the left" continues to make it exceedingly more difficult for law abiding citizens to acquire firearms
More specifically, Democratic lawmakers in general, yes. But not all people that tend to vote Democratic believe that; I vote democratic because I also strongly support abortions rights, LGBTQ+ rights, tax reform, major criminal justice/policing/rehabilitation reform, single-payer health care, etc. I'm not a single issue voter. But if more people that identify as Democratic get involved in shooting, we're more likely to see Democratic politicians start changing their stances. Having a place where people that are on the left can talk, and be supportive of gun rights while also supporting things that are more traditionally seen political left point should help, over time.
Personally, I'd consider myself more right leaning, because I want 2A rights...
That alone doesn't make you on the political right. The fastest growing demographic for new gun owners is black people, but black people overwhelming vote on the political left--or for Democratic candidates, at least--because the left has more to offer them. Gun ownership is part of a spectrum of issues that may help define where you are, but isn't the single determinant by itself. You say, for instance, that you're pro-LGBTQ, pro-women's equality (which is broadly consistent with 2nd wave feminism at a minimum), etc. These are things that the political right are generally opposed to; when DeSantis says that Florida is where woke goes to die, those are the things he's in opposition to. I don't think that it's a stretch to say that any of the current Republican presidential candidates (Trump, DeSantis, Pence, Haley, Scott, Ramaswamy, Christie, Hutchinson, Elder, or Burgum) are in favor of any LGBTQ rights, and all of them appear to want to significantly curtail the rights of transgender people. All of them were in favor of eliminating the reproductive choices of women.
I disagree with Democrats--which comprise the bulk of the US political left--on 2A issues.
without 2A, none of the aforementioned policies would be defensible.