Replace the code below of bxcft_edit_render_new_xprofile_field function:
elseif ( bp_get_the_profile_field_type() == 'datepicker' ) {
?>
<div class="input-web">
<label class="label-form <?php if ( bp_get_the_profile_field_is_required() ) : ?>required<?php endif; ?>" for="<?php bp_the_profile_field_input_name() ?>"><?php bp_the_profile_field_name() ?> <?php if ( bp_get_the_profile_field_is_required() ) { echo __('*', 'bxcft'); } ?></label>
<input type="date" name="<?php bp_the_profile_field_input_name() ?>" id="<?php bp_the_profile_field_input_name() ?>" <?php if ( bp_get_the_profile_field_is_required() ) : ?>aria-required="true" required="required"<?php endif; ?> class="input" value="<?php bp_the_profile_field_edit_value() ?>" />
</div>
<?php
}
By this code:
elseif ( bp_get_the_profile_field_type() == 'datepicker' ) {
if (bp_get_the_profile_field_edit_value() != '')
$value = bp_get_the_profile_field_edit_value();
else
$value = 'put your default date here';
?>
<div class="input-web">
<label class="label-form <?php if ( bp_get_the_profile_field_is_required() ) : ?>required<?php endif; ?>" for="<?php bp_the_profile_field_input_name() ?>"><?php bp_the_profile_field_name() ?> <?php if ( bp_get_the_profile_field_is_required() ) { echo __('*', 'bxcft'); } ?></label>
<input type="date" name="<?php bp_the_profile_field_input_name() ?>" id="<?php bp_the_profile_field_input_name() ?>" <?php if ( bp_get_the_profile_field_is_required() ) : ?>aria-required="true" required="required"<?php endif; ?> class="input" value="<?php echo $value; ?>" />
</div>
<?php
}
Tell me if this works.