I think anyone reading the laws the bill modifies could reasonably come to that conclusion.
According to the text of the Canadian Human Rights Act:
It is a discriminatory practice, directly or indirectly... in the
course of employment, to differentiate adversely in relation to an
employee, on a prohibited ground of discrimination.
and:
It is a discriminatory practice in the provision of goods, services,
facilities or accommodation customarily available to the general
public... to differentiate adversely in relation to any individual, on
a prohibited ground of discrimination.
and:
It is a discriminatory practice, in the provision of goods, services,
facilities or accommodation customarily available to the general
public... or in matters related to employment, to harass an individual
on a prohibited ground of discrimination.
It could easily be argued that using an "incorrect" pronoun means they are "differentiating adversely" in relation to that employee and/or customer.
According to the Canadian Bar Association, the pronoun use debate is a "misunderstanding", but they also say:
In federally regulated workplaces, services, accommodation, and other
areas covered by the CHRA, it will constrain unwanted, persistent
behaviour (physical or verbal) that offends or humiliates individuals
on the basis of their gender identity or expression.
But using a "wrong" pronoun could easily "offend" someone, it would be "unwanted", and it would be "persistent" unless people changed which pronouns they say.
There's also this section in the Canadian Human Rights Act:
(1) Subject to subsection (2), any act or omission committed by an
officer, a director, an employee or an agent of any person,
association or organization in the course of the employment of the
officer, director, employee or agent shall, for the purposes of this
Act, be deemed to be an act or omission committed by that person,
association or organization.
(2) An act or omission shall not, by virtue of subsection (1), be
deemed to be an act or omission committed by a person, association or
organization if it is established that the person, association or
organization did not consent to the commission of the act or omission
and exercised all due diligence to prevent the act or omission from
being committed and, subsequently, to mitigate or avoid the effect
thereof.
The effect of that is, an employer is going to be held responsible for the actions of its employees unless they take "all due diligence" to prevent the action. If one employee refuses to use the preferred pronoun of another employee (or customer), I'm not sure how a company could avoid needing to discipline the employee for not using the pronoun.
It's true that nobody can actually order them to fire the employee:
No order that is made under subsection 53(2) may contain a term
requiring the removal of an individual from a position if that
individual accepted employment in that position in good faith.
But that barely matters. The company is going to be facing liability if they employ both people, and it's legally prohibited to retaliate against the one making the complaint, so guess who is going to get the boot.
And finally, I note this section:
In addition to any order under subsection (2), the member or panel
may order the person to pay such compensation not exceeding twenty
thousand dollars to the victim as the member or panel may determine if
the member or panel finds that the person is engaging or has engaged
in the discriminatory practice wilfully or recklessly.
The prospect of increased punishment for willful or reckless discrimination implies that behavior which is neither willful nor reckless can also be punished, just not with the enhancement. This is likely to make companies paranoid.
It's true that this mostly applies only at work - however, we're at work for a rather large portion of our waking hours.