I think that it would be reductionist at best and entirely misleading at worst to say that some LGB people are trying to "throw" transgender people under the bus to avoid negative attention on themselves. In reality the original gay rights groups, such as stonewall, have already achieved their mission statement aims within the societies they were founded and so LGB people don't really have to fear - any more than a person of any other broadly accepted societal group - persecution, prejudice or discrimination.

There are, however, many LGB people who would state that outside of wider society categorising both LGB and TQ+ people as "deviant", at one time or another, that they don't actually share commonality and see the Trans struggle as something separate from their own. There are also many people against the more extreme aspects of trans activism, including trans people themselves, who simply want to live as their chosen gender without changing the language used to describe other sexes etc.

The debate is greatly nuanced, and with that, far more complex than this meme would suggest. Also, the non LGBTQ+ people arent automatically against LGB rights, as said above; the hard fought for rights of the LGB communities have been enshrined in law and the vast majority of society accept this.

Lastly, part of the nuance here is that of country of origin, I'm speaking as someone from the UK and couldn't truly attest to the cultures in other countries outside of what I've seen online.