Irrelevant. One share, one vote. If you want to back your views with your own money, put it all into BA shares. If not, accept that someone else has put up money, which is at risk, and for which they want a return.
If the private shareholders outnumbered the pension funds and investment managers, that would be their choice and they would have comparable influence.
As I said above, that money is from pension funds, funding retirement funds for many UK pensioners. Ultimately, they want the best return.
Private shareholders at BA are not 0.5% of shareholders; thus >99% in favour of management also indicates a majority of private shareholders are also in favour of management.