Thanks for the screenshots, they do help. The page shown (General Settings) looks very similar to a page that is provided by the BuddyPress Groups Extras (BPGE) plugin, see the following screenshot:

As indicated in the screenshot, the Home or, in your case, the
Activities tab is fixed in place by the code:
if ( $nav['slug'] === 'home' ) {
$disabled = 'ui-state-disabled';
}
The above snippet can be found here and just indicates that the Home tab is disabled from being sortable. The following is what the element (li) has as classname (default ui-state-disabled
) for a non sortable tab of which the only one is the Home tab.
<li id="position_686f6d65" class="default ui-state-disabled">
<strong>Home</strong>
</li>
While a sortable tab has default ui-sortable-handle
as a classname.
<li id="position_6d656d62657273" class="default ui-sortable-handle" style="">
<strong>Members <span>1</span></strong>
</li>
The BPGE plugin author claims this change was due to:
Group's "Activity"/"Home" navigation link is hard coded in BuddyPress to always be the first one, so disable its reordering.
However, when I rollback from v3.7.0 to v3.6.10, the Home tab is now sortable and can be moved. So the reason for the change is not entirely true.
Moving along, since the General Settings page from the BPGE plugin is similar to the page from your screenshots, we may be able to infer that there was a fork of some the code (the pages portion) from the BPGE plugin and was included in the BuddyBoss theme which AFAIK is a commercial (paid) theme, meaning I can’t verify the code within this theme due the status of free vs paid. If this is the case, then your resolve will have to come from the BuddyBoss developers. However, if the code that supports manage Page general setting resides elsewhere, e.g., custom code or 3rd party plugin, then the resolve is the responsibility of those who authored the code.
As an aside, as it relates to the BPGE plugin, there is an appearance of wonkiness with the reordering of group tabs which appears to be a factor that caused the change to make the Home tab not sortable, however, I’m not sure if BuddyPress is causing the wonkiness,
Having stated all of the above, it seems to me, the reason that you want the Pages tab to be the first tab is because you want that to be the landing page. Would this be a correct assumption? If so, there may be the possibility of changing the landing page to Pages, regardless of the tab order, which will depend on similar the code is similar enough to the BPGE plugin.