The "mutualists" and the "left-libertarians" oppose using the term "capitalism," not because of the negative denotations or connotations, but because they oppose the exclusive ownership of capital goods.
Francois Tremblay said two statements that conflicted with mutualism:
Capitalists, on the other hand, complain that mutualists don’t believe in perpetual property rights, and use this to dismiss mutualism altogether.
If use/occupancy rules were applied right now, there is no doubt that the whole system of capitalism, based on private owners of the means of production who have no use/occupancy connection with them (including land), would be gone by tomorrow.
However, mutualists do not oppose the "perpetual ownership of the capital goods (or the means of production)." Benjamin Tucker only opposes the perpetual ownership of land. In all other things, however, he opposes the use-and-possession laws. As he wrote in State Socialism and Anarchism:
Proudhon scoffed at this distinction between capital and product. He maintained that capital and product are not different kinds of wealth, but simply alternate conditions or functions of the same wealth; that all wealth undergoes an incessant transformation from capital into product and from product back into capital, the process repeating itself interminably; that capital and product are purely social terms [...] But, though opposed to socializing the ownership of capital, they aimed nevertheless to socialize its effects by making its use beneficial to all instead of a means of impoverishing the many to enrich the few. And when the light burst in upon them, they saw that this could be done by subjecting capital to the natural law of competition, thus bringing the price of its own use down to cost
Thus, Francois Tremblay's advocacy of implementing the use-and-occupancy laws on all capital goods contradict the mutualists' position, even with Proudhon's.
Forcibly supporting the compulsory use-and-occupancy laws on capital goods, however, will distort the rational allocation of resources in the economy. Let us demonstrate the effects of forcing the use-and-occupancy laws on capital.
First, forcing the use-and-occupancy laws on capital is equivalent to forcing others to borrow capital at zero percent interest. This would disrupt the price signals of capital goods, which would cause a misallocation of capital goods in the economy. Forcing the use-and-occupancy laws on capital would disrupt the free price system, as described by the marginal theory of value.
The mutualists do not appear to understand the "marginal theory of value." However, understanding the "marginal theory of value" is a prerequisite for understanding the free price system and the economic calculation problem. Thus, the mutualists do not have a complete understanding of the economic calculation problem.
Forcing the use-and-occupancy laws on capital would have a few of the same effects from the economic calculation problem, as in state-socialism. Unfortunately, Kevin Carson redefined mutualism as a decentralized version of state-socialism.
The self-identified "mutualists" misinterpret their philosophy as opposing the exclusive ownership of all capital goods. Thus, they oppose the term "capitalism" because they oppose the exclusive ownership of capital goods. As shown, forcing the occupancy-and-use laws on capital goods, however, will result in a misallocation of capital goods, which will have a few of the deleterious effects as described by the economic calculation problem.
The "non-mutualist" "left-libertarians" oppose capitalism for a different reason. They claim that the definition of "capitalism" does not equal the free market. The "non-mutualist" "left-libertarians" also oppose the word "capitalism" because since they ally with the "mutualists," they must drop the term "capitalism" in order to communicate effectively with the mutualists. Therefore, the "left-libertarians," who ally with the "mutualists," must, also, abandon the term "capitalism" to keep their alliance with the "mutualists." The self-identified "mutualists" also have a flawed gradualist strategy.