What it has to with the LGB is the long standing, pernicious and harmful lie that gay people are deviant and paedophiles by nature.
This has nothing to do with people who identify as trans. Many people who identify as trans are not LGB. Most late transitioning males are heterosexual. Most are married to or in relationships with women. Many of them have fathered children with those women.
That same lie is continuing to be peddled under the guise of the threat from trans predators.
The threat from trans predators is real. Obviously not all people who identify as trans are predators, but some males who identify as trans are. The threat which we are concerned about is male people who identify as trans and who are being enabled in their crimes by people who are going along with their wishes to be treated as women and being allowed in women-only spaces. What these predators all have in common is that they are male. It's nothing to do with their sexuality, but most of them appear to be heterosexual. So it's nothing to do with LGB.
When someone like GL posts saying "these MPs all wants to hurt kids" he's pushing that same lie, that kids are at risk from all trans people (and by extension gay people because of the LGBT).
You don't seem to have understood the context of that tweet. The context about protecting kids is about protecting them from unnecessary and harmful medical treatment, not being protected from trans people.