I don't really understand the argument that "funding" gives Mermaids standing in this particular claim. Mermaids has a particular cause, raising money to help trans people and their families and their belief in a gender-based identity, and the ensuing medical "needs" of that group. LGBA's cause relates to the welfare of LGB people, and their right to be attracted to, and engage in. sexual relationships with other people sharing the same biological sex, no medical needs involved. These are 2 very distinct causes.
People minded to donate to LGBA are not going to be donating to Mermaids for the same reasons they would otherwise donate to the LGBA, because they are not both covering the same causes. That is not to say the same people who would donate to LGBA (to protect same sex attraction) wouldn't also donate to Mermaids, but they would donate to Mermaids for a different reason (because they want to assist trans people and their families). It's not necessarily incompatible to support them both, but in supporting them both, you are not doing so for the same reasons.
Therefore, Mermaids claiming that both organisations are competing for the same funding necessarily must include the implied claim that members of the public are too stupid to know what they are donating their money for/to; and/or are incapable of making a considered decision, so one charity must go; and/or that people will chuck their money at anyone without really thinking about why. That's a pretty contemptible way to view your donors, and it's not something I would be shouting about if I was Mermaids.