I am using this code:

g_signal_connect(showapp_option, "activate", G_CALLBACK(&MainWindow::show_app), appindicator);

warning: converting from 'void (MainWindow::*)()' to 'GCallback {aka void (*)()}' [-Wpmf-conversions]

We need to see more context.

Ok, here it is:

void MainWindow::show_app(){
    //crash here:
    this->show();
    //this works fine:
    app_indicator_set_status(appindicator, APP_INDICATOR_STATUS_PASSIVE);

}

void MainWindow::make_indicator()
{
    if(appindicator){
        //appindicator has already been created
        return;
    }
    appindicator = app_indicator_new("Format Junkie Indicator", "formatjunkie", APP_INDICATOR_CATEGORY_APPLICATION_STATUS);
    GtkWidget* showapp_option;
    GtkWidget* add_audio_option;
    //GtkWidget* subitem3;
    GtkWidget* indicatormenu = gtk_menu_new();
    GtkWidget* item = gtk_menu_item_new_with_label("Format Junkie main menu");
    gtk_menu_item_set_submenu(GTK_MENU_ITEM(item), indicatormenu);

    showapp_option = gtk_menu_item_new_with_label("Show App!");
    g_signal_connect(showapp_option, "activate", G_CALLBACK(&MainWindow::show_app), appindicator);
    gtk_menu_shell_append(GTK_MENU_SHELL(indicatormenu), showapp_option);

    add_audio_option = gtk_menu_item_new_with_label("Add audio files");
    g_signal_connect(add_audio_option, "activate", G_CALLBACK(&MainWindow::add_audio_files), appindicator);
    gtk_menu_shell_append(GTK_MENU_SHELL(indicatormenu), add_audio_option);
/*
    subitem3 = gtk_menu_item_new_with_label("Quit");
    g_signal_connect(subitem3, "activate", G_CALLBACK(quit_from_indicator), appindicator);
    gtk_menu_shell_append(GTK_MENU_SHELL(menu), subitem3);*/
    gtk_widget_show_all(indicatormenu);
    app_indicator_set_status(appindicator, APP_INDICATOR_STATUS_ACTIVE);
    app_indicator_set_attention_icon(appindicator, "dialog-warning");

    app_indicator_set_menu(appindicator, GTK_MENU (indicatormenu));
}

You are forcing a conversion from a class member to a function call. Class members have this, function calls don't. So it crashes.

If you make the member function static, you'll be able to call it, since static member functions don't have 'this'. So you won't have this but you can make do -- that's what the data parameter in a GTK callback is for instead. You can pass a long a pointer for data you need later. Pass in the class itself and you can go datapointer->whatever.

// You'll have to change the definition in the header file too, if any
static void MainWindow::show_app(MainWindow *data){
    data->show();
    //crash here:
//    this->show();
    //this works fine:
    app_indicator_set_status(appindicator, APP_INDICATOR_STATUS_PASSIVE);
}

void MainWindow::make_indicator()
{
    if(appindicator){
        //appindicator has already been created
        return;
    }
    appindicator = app_indicator_new("Format Junkie Indicator", "formatjunkie", APP_INDICATOR_CATEGORY_APPLICATION_STATUS);
    GtkWidget* showapp_option;
    GtkWidget* add_audio_option;
    //GtkWidget* subitem3;
    GtkWidget* indicatormenu = gtk_menu_new();
    GtkWidget* item = gtk_menu_item_new_with_label("Format Junkie main menu");
    gtk_menu_item_set_submenu(GTK_MENU_ITEM(item), indicatormenu);

    showapp_option = gtk_menu_item_new_with_label("Show App!");
    g_signal_connect(showapp_option, "activate", G_CALLBACK(&MainWindow::show_app), this);
    gtk_menu_shell_append(GTK_MENU_SHELL(indicatormenu), showapp_option);

    add_audio_option = gtk_menu_item_new_with_label("Add audio files");
    g_signal_connect(add_audio_option, "activate", G_CALLBACK(&MainWindow::add_audio_files), this);
    gtk_menu_shell_append(GTK_MENU_SHELL(indicatormenu), add_audio_option);
/*
    subitem3 = gtk_menu_item_new_with_label("Quit");
    g_signal_connect(subitem3, "activate", G_CALLBACK(quit_from_indicator), appindicator);
    gtk_menu_shell_append(GTK_MENU_SHELL(menu), subitem3);*/
    gtk_widget_show_all(indicatormenu);
    app_indicator_set_status(appindicator, APP_INDICATOR_STATUS_ACTIVE);
    app_indicator_set_attention_icon(appindicator, "dialog-warning");

    app_indicator_set_menu(appindicator, GTK_MENU (indicatormenu));
}

Thanks for this! Still, it doesn't work!
This is my code:

void MainWindow::show_app(MainWindow *data){
    data->show();
    app_indicator_set_status(appindicator, APP_INDICATOR_STATUS_PASSIVE);
}

void MainWindow::make_indicator()
{
    if(appindicator){
        //appindicator has already been created
        return;
    }
    appindicator = app_indicator_new("Format Junkie Indicator", "formatjunkie", APP_INDICATOR_CATEGORY_APPLICATION_STATUS);
    GtkWidget* showapp_option;
    GtkWidget* add_audio_option;
    //GtkWidget* subitem3;
    GtkWidget* indicatormenu = gtk_menu_new();
    GtkWidget* item = gtk_menu_item_new_with_label("Format Junkie main menu");
    gtk_menu_item_set_submenu(GTK_MENU_ITEM(item), indicatormenu);

    showapp_option = gtk_menu_item_new_with_label("Show App!");
    g_signal_connect(showapp_option, "activate", G_CALLBACK(&MainWindow::show_app), this);
    gtk_menu_shell_append(GTK_MENU_SHELL(indicatormenu), showapp_option);

    add_audio_option = gtk_menu_item_new_with_label("Add audio files");
    g_signal_connect(add_audio_option, "activate", G_CALLBACK(&MainWindow::add_audio_files), this);
    gtk_menu_shell_append(GTK_MENU_SHELL(indicatormenu), add_audio_option);

    gtk_widget_show_all(indicatormenu);
    app_indicator_set_status(appindicator, APP_INDICATOR_STATUS_ACTIVE);
    app_indicator_set_attention_icon(appindicator, "dialog-warning");

    app_indicator_set_menu(appindicator, GTK_MENU (indicatormenu));
}

private slots:
    static void show_app(MainWindow *data);

error: cannot declare member function 'static void MainWindow::show_app(MainWindow*)' to have static linkage [-fpermissive]

The warning is a warning. If you know why it's there and what you're doing, you can ignore it.

It's saying -fpermissive might allow you to follow that suggestion but it might not be a good idea. I think that used to be perfectly valid, but standards are changing, so let's follow its suggestion and do that another way. Let's make global functions instead of static ones...

// Completely outside the class
void show_app_stub(MainWindow *data)
{
        data->show_app();
}

...

// in make_indicator
g_signal_connect(showapp_option, "activate", G_CALLBACK(show_app_stub), this);

Thanks again. The warning's gone but the crush is still there...