There are two misconceptions in this question. First, that every stance a politician can take fits into a conservative/libertarian dichotomy. A political action can also be both or neither.
Second, that conservative and libertarian are opposed. They are not. They are orthogonal concepts.
Conservative means "The inclination, especially in politics, to maintain the existing or traditional order". Or in other words "doing things the way we always did them". This is opposed to Progressivism, which means "A political ideology that favours progress towards better conditions in society" or "let's try something new".
A pure gender segregation in bathrooms based on biological sex assigned from birth was the way Americans were always doing it. Acknowledging and accommodating transsexuality is a rather new concept for the US-american society. This makes it a progressive concept. So the stance that society should not support transsexuality is a conservative position.
Libertarianism is a political concept which (overly simplified) says that personal freedoms and rights should be maximized, including rights to one's own property. The opposite is Authoritarianism, which says that the government should have the authority to decide how people live.
Now what would be the authoritarian and what the libertarian position in the trans bathroom issue?
Libertarianism guarantees property rights. If someone wants to use your property, like your bathroom, then you have the right to state the conditions for that or forbid it altogether. You are not required to justify your decision in any way, because it's your property and you alone decide what happens with it. So the libertarian position would be that every owner of two or more public bathrooms can decide who is allowed to use which one.
Authoritarianism gives authority to the state. So no matter if the state says "everyone has to allow everyone to use whatever bathroom they want" or "we say who can use which bathroom", both are authoritarian positions.
Now what's Trump's position? In a talk show a year ago he criticized a new law in North Carolina which strengthened the traditional gender segregation in bathrooms. This was a conservative law, so his position here could be called progressive.
But is his stance authoritarian or libertarian? That depends on how he intends to solve the issue. Leaving the decision to individual bathroom owners would be libertarian. Advocating a government-imposed bathroom etiquette would be authoritarian. But as the source from the answer by tim mentions, he doesn't seem to have a strong position on this issue anymore. Otherwise he wouldn't delegate it to the state level and let them decide for themselves if they pick the authoritarian-conservative, the authoritarian-progressive or the libertarian solution.
