[angeldimmon]

Is da'wah fee sabeelillah supposed to be restricted to people within own's madhhab???

This question is also answered in the answer on Beard from Sunnipath by Sheikh Amjad:

The Impermissibility of Commanding the Right
and Forbidding the Wrong in Matters of Disagreement

I would like to conclude this answer by mentioning that the rulings
of commanding the right and forbidding the wrong only apply to
matters that are agreed upon among scholars as being obligatory
or unlawful. As for something that is differed upon, such as the issue
under discussion, it is not permissible to condemn someone for doing it.
It is, however, recommended for one to give sincere advice to such a
person and to encourage him to adopt the more religiously precautionary
position by extricating himself from the disagreement of the scholars.

The great scholar, the Proof of Islam, Imam Ghazali said in the Ihya during
his discussion of the integrals and conditions of commanding the right,

"The fourth condition is that the matter being condemned be something
that is condemnable without being subject to scholarly disagreement.
Commanding the right and forbidding the wrong does not apply to anything
that falls under the realm of scholarly disagreement. It is therefore not
permissible for a follower of the Hanafi school to condemn a follower of
the Shafi`i school for eating a lizard, a hyena, or meat upon which the
name of Allah was not pronounced [even though such matters may be
unlawful in the Hanafi school]."

Imam Nawawi said in his commentary on Sahih Muslim,

Scholars only condemn what is agreed upon [as being unlawful].
As for something that is differed upon, it may not be condemned because
either (a) the conclusion of every mujtahid is correct—and this is the
position adopted by many (or most) of the scholars of exacting
verification—or (b) only one of them is correct but we don’t know with
certainty which one is incorrect and [whoever he may be] he is not
sinful [for reaching his incorrect conclusion].

However, if one encourages such a person to extricate himself from
scholarly disagreement by way of giving sincere advice, then this is
a good and praiseworthy thing when done with gentleness. This is
because scholars agree that is encouraged to extricate oneself from
scholarly disagreement when doing so does not result in contravening
a sunna or falling into another disagreement.

And Allah Most High knows best what the correct position is and to
Him is the final return.

[end excerpt]

Wallaahu A'lam.