I would refactor it to something like:

import { merge } from 'rxjs';
import { map } from 'rxjs/operators';
...

const forwardProp = prop => value => ({prop, value});

const obs = [
    this.reportPropertiesChanges$.pipe(map(forwardProp('reportProperties'))),
    this.objectsProperties$.pipe(map(forwardProp('reportObjectsProperties'))),
    this.textPropertiesChanges$.pipe(map(forwardProp('textProperties'))),
    this.toggleLabels$.pipe(map(forwardProp('visibleText')))
];

merge(...obs).pipe(filter(() => this.loaded)).subscribe(({prop, value}) => {
  this.registryReportSettings[prop] = value;
  this.registryReportSettings$.next(this.registryReportSettings);
});

You can use merge, which will trigger if any Observable will emit a value

this.reportPropertiesChanges$.pipe(map(reportProperties => ({reportProperties})));
this.objectsProperties$.pipe(map(reportObjectsProperties => ({reportObjectsProperties})));
this.textPropertiesChanges$.pipe(map(textProperties => ({textProperties})))
this.toggleLabels$.pipe(map(visibleText => ({visibleText})));

merge(
    this.reportPropertiesChanges$,
    this.objectsProperties$,
    this.textPropertiesChanges$,
    this.toggleLabels$
)
.pipe(
    filter(() => this.loaded)
).subscribe((p) => {
    this.registryReportSettings = {...this.registryReportSettings, ...p };
    this.registryReportSettings$.next(this.registryReportSettings);
});

You can use combineLatest operator from rxjs as well. It will give you access to all the 4 subscribables in one operator. Something like this:

const reportProps = this.reportPropertiesChanges$;
const objectsProperties = this. objectsProperties$;
const textPropertiesChanges = this.textPropertiesChanges$;
const toggleLabels = this. toggleLabels$;

combineLatest([
   reportProps,
   objectsProperties,
   textPropertiesChanges,
   toggleLabels
]).pipe(filter(() => this.loaded)).subscribe(([
     reportPropsValue, 
     objPropsValue,
     textChangesValue,
     toggleLabelsValue
   ]) => {
      this.registryReportSettings.reportProperties = reportPropsValue;
      this.registryReportSettings.reportObjectsProperties = objPropsValue;
      this.registryReportSettings.textProperties = textChangesValue;
      this.registryReportSettings.visibleText = toggleLabelsValue;

      // Once you set all the values, you can update the Behavior Subject
      this.registryReportSettings$.next(this.registryReportSettings);
   })