What you are saying is absolutely liberalism. If you don't understand why cops are not working class, then you don't understand class conflict and if you don't understand class conflict, then you are not a leftist.
Class is a person's relationship to labor and the means of production. The defining characteristic of being working class is doing productive labor while not owning the means of production. A working class person uses their labor to create commodities or services which they do not own.
Cops do not do productive labor. Cops do not produce anything. Cops are not exploited by the bourgeoisie. Cops are guard labor and guard labor is worthless.
Here is an excerpt from chapter 13 of Marx's Capital.
The directing motive, the end and aim of capitalist production, is to extract the greatest possible amount of surplus-value, [14] and consequently to exploit labour-power to the greatest possible extent. As the number of the co-operating labourers increases, so too does their resistance to the domination of capital, and with it, the necessity for capital to overcome this resistance by counterpressure. The control exercised by the capitalist is not only a special function, due to the nature of the social labour-process, and peculiar to that process, but it is, at the same time, a function of the exploitation of a social labour-process, and is consequently rooted in the unavoidable antagonism between the exploiter and the living and labouring raw material he exploits.
Again, in proportion to the increasing mass of the means of production, now no longer the property of the labourer, but of the capitalist, the necessity increases for some effective control over the proper application of those means. [15] Moreover, the co-operation of wage labourers is entirely brought about by the capital that employs them. Their union into one single productive body and the establishment of a connexion between their individual functions, are matters foreign and external to them, are not their own act, but the act of the capital that brings and keeps them together. Hence the connexion existing between their various labours appears to them, ideally, in the shape of a preconceived plan of the capitalist, and practically in the shape of the authority of the same capitalist, in the shape of the powerful will of another, who subjects their activity to his aims. If, then, the control of the capitalist is in substance two-fold by reason of the two-fold nature of the process of production itself, which, on the one hand, is a social process for producing use-values, on the other, a process for creating surplus-value in form that control is despotic. As co-operation extends its scale, this despotism takes forms peculiar to itself. Just as at first the capitalist is relieved from actual labour so soon as his capital has reached that minimum amount with which capitalist production, as such, begins, so now, he hands over the work of direct and constant supervision of the individual workmen, and groups of workmen, to a special kind of wage-labourer. An industrial army of workmen, under the command of a capitalist, requires, like a real army, officers (managers), and sergeants (foremen, overlookers), who, while the work is being done, command in the name of the capitalist. The work of supervision becomes their established and exclusive function. When comparing the mode of production of isolated peasants and artisans with production by slave-labour, the political economist counts this labour of superintendence among the faux frais of production. [16] But, when considering the capitalist mode of production, he, on the contrary, treats the work of control made necessary by the co-operative character of the labour-process as identical with the different work of control, necessitated by the capitalist character of that process and the antagonism of interests between capitalist and labourer.
This excerpt tells us that the exploitation of productive labor on a large scale requires a "real army" to prevent workers from taking control due to the opposing interests between the capitalist and laborer. The excerpt tells us that this is a "special kind" of wage-labourer ie not a productive labourer, not working class. The excerpt tells use that this kind of laborer is "faux frais of production", meaning that this person does not add value to production. The excerpt tells us that the role is the person is to control the antagonism of interests between the capitalist and working class.
The class interest of police is aligned with the capitalist class interests. The class interest of the police is prevent the working class from gaining power. The police of the capitalist state exist to prevent socialism from happening.
There is importance in understanding that cops are not working class because when you organize working class people, you have to be aware that the police will be working against you 100% of the time. It's not a "moral reasoning". It is materialist analysis.
Part of gaining class consciousness is recognizing that your own productive capacity is being exploited. The capitalist takes value from what you create and gives you less than the value you generated. Cops do have productive capacity and are not exploited. Cops are part of the exploitation process.
Did you seriously compare cops to baristas? Baristas make coffee. Police make nothing. Baristas serve coffee. Police use violence to enforce the will of the capitalist class. Some baristas work for a capitalist and some baristas are artisans who own their own coffee show, they could either be a worker or a small business owner. Police serve the interests of the bourgeois state. Stop going on twitter. Stop doing twitter discourse. Stop posting twitter discourse on hexbear.
The Marx quote is not a direct comparison because police as we know them today did not exist during the time of Marx's life. However the passage matches the characteristics of police as we know them today.
Managers and supervisors are often considered to be petite bourgeoisie depending on the amount of authority that they have in a company. Cops are part of the state and the state acts in the interests of the capitalist class.
The Engels quote you posted is saying that the working class of pre-capitalist economies were not proletarian, because the proletariat is specifically the working class of the capitalist economy. The working class that the Engels quote is referring to is slaves and peasants of past economies, ie slave society and feudalism. Slaves and peasants still had productive capacity but did not receive a wage for their productive capacity. The defining characteristic of the working class is still productive capacity. The additional characteristic of the proletariat is receiving a wage for the production. Cops do not produce. Cops receive a wage but not produce. Cops are not working class.