Will distance education get a teaching job

If the University offering the course is a recognised University and the course is an approved course by UGC even a degree obtained by distance education is treated equally to the degree obtained as a regular student. So regarding eligibility for a teaching post, there will not be any problem. But after obtaining LLM or MA in Sociology, you have to write the Entrance Test for the lecturership in government college with all benefits as per UGC norms.
Alternatively, you have to join as a lecturer in a private college where the remuneration will be less and you have to work for your PhD on a part-time basis. Once you complete your PhD you will become eligible for lecturership with all benefits. You need not write the entrance test but you should get selected in an oral examination.

If the university and it's courses are recognized by UGC then there is no problem for the acceptance of your degree for appointment as an teacher.

For getting an appointment as lecturer or Assistant Professor in a college one has to either qualify in NET test or complete Ph.D. Only after qualifying NET test you are eligible to apply for a lecturer job.

Alternatively, if you can complete Ph.D then you need not to qualify in NET and can apply for lecturer ship.

Please remember that there is a large rush of people for jobs and especially teaching jobs which are thought to be academic and provide a calm and quite job environment. So one has to put a lot of efforts for performing nicely in the interviews and counselling sessions for selection to the coveted post of lecturers.

The distance mode of education is not likely to hamper your career - prospects provided it is recognised by the University - grant commission and by tracking down the affiliation of UGC mode, one can go ahead with such courses.
There are recognised universities offering the education through distance mode but are well recognised in terms of UGC status such IGNOU, Manipal - distance education, Karnataka Open University, Utkal University Distance - education etc and the degrees persued from such universities is not going to dilute the standard of the degrees imparted by such institutions.
With respect to your entry as an associate professor, there are two ways - the first one being a NET qualifier by securing a minimum 55 percent in the post - graduate level and then passing the NET examination conducted by CBSE twice in a year or resorting to second option where you will be required to obtain a Ph.D degree from an eminent university with an able guide and your published work should be of high standard. You may look out the advertisement published in some leading News Papers where you may notice the vacancies of lecturers, associate - professors etc. Your selection would depend upon your satisfactory performance in the interview.
You can also join a private college and can carry out your Ph.D under the guidance of a reputed professor and in that way, you can earn a good remuneration and a doctorate degree can be achieved which will ultimately widen your career in the educational- field.

The valid distance learning course or degree is always acceptable for teaching jobs. You can even pursue higher study based on the distance learning degree. Once you achieve your higher degree from regular mode, the basic distance learning degree does not matter most. You will be qualified based on your latest regular degree.

If your percentage in the Post-Graduation is very good and if you clear the NET for lectureship in your subject, you will have equal opportunity for lectureship/assistant professorship in Government colleges. However, I admit that in case of private educational institutions, you may face some problems, because such institutions don't bother much about equal opportunity and UGC recognition, etc. So, you must give preference to get an appointment in Government colleges.

Masters from a UGC recognized University or college is accepted by Government norms for appointment and promotion provided other regular criteria are met.

The LLM from Directorate of distance education, Kurukshetra University is recognized by UGC and is NAAC accredited with Grade 'A'. It is also listed under the state universities in UGC website (https://www.ugc.ac.in/stateuniversitylist.aspx?id=8&Unitype=2).

The MA sociology from IGNOU does not need much explanation about its recognition.(https://www.indiatoday.in/education-today/news/story/ugc-distance-degree-264252-2015-09-22).

With regards to your appointment as assistant professor, you need a good academic track record, the UGC NET/SET exams and it would be desirable for publications and research work/ books. Most common appointments would start as a lecturer and move on to assistant professor and above.

So, there is no need for concern, focus on the studies, gaining experience, publish papers and then the NET/SET exams would lead you to the Assitant Professor job that you desire. Of course, if you also finish your PhD, then you would be exempted from the NET/SET exams.