Was Martin Luther King Jr a conservative?

No, he was not a 'conservative' because part of the definition of conservative is...being against change. 

MLK was all about civil rights and equality for Black Americans/ people of color. This would be huge change for the then society of the US. So, he was totally for a major change. So, no conservative.

He was otherwise traditional socially and nationally so what he was, was a 'progressive' of the type of Theodore Roosevelt. 'Progressives' by this old definition were those like Theodore and MLK who were... traditional and liked the country pretty much the way it was but wanted to change one big thing...Roosevelt get rid of monopolies....MLK get rid of racism and segregation.

*P.S. since the 1980's in the US current day politicians have been misusing these words to relabel/ rebrand themselves to suit their modern day politics and mislead the public to really what they are. By the real definitions here's some examples of who people really were (are).

Ronald Reagan...no 'conservative' but reactionary (he wanted to take things back to a more old fashioned time).

George H.W. Bush (the 1st Bush)/ Dwight Eisenhower...conservatives.

Liberal...Hillary Clinton

Moderate...Obama and Bill Clinton

Leftist/ Socialist...Bernie Sanders

Radical...AOC (Alexandria Ocasio Cortez) and friends.

Communist...the US never had any/ still doesn't.  

Neoliberalism...the right wing of the Republican party not new or liberal at all but unleashing the rich to rule everyone, Reaganomics/ nationalism/ militarism.  

Yes, but back in the 60s that meant something fairly different. As much as people might deny this, MLK would go over like a lead balloon in today's GOP. 

He certainly saw the hypocrisy of the Democrat Party and did not join.

He was socially conservative no doubt 

Conservatism comes in different forms.  As an example one can be a fiscal conservative and a social liberal and vice versa. There are some who are both fiscal and social conservatives. There are also varying degrees of conservatism ranging from centre-right to extreme right. 

It is important that people don't know what such words mean or what they historically meant. If people knew and understood such things they would be very hard to manipulate.