As a proof to this opinion, these Poskim cite the 5th Ani Ma’amin of the Rambam (13 principles of faith written by Maimonides) which explicitly says "I believe...that only to Hashem is it proper to daven and not to anyone else".
Accordingly, these Poskim frown upon those who frequent graves of Tzadikim and daven there, as it may seem as if they are davening "to" the Tzadik, as opposed to asking the Tzadik to be a "Meilitz Yosher- a good advocate" for them in Shamayim.
However, many Poskim (Rav Shlomo Zalmen Auerbach and others) are of the opinion that it is OK to beseech the "Machnisei Rachamim- the angels whose specific task it is to bring the requests for mercy before Hashem" to do their task and take our prayers to Hashem. We aren’t praying to the angels, rather we are asking them to be our messengers to properly place our prayers in the right sequence and at the right time to Hashem.
They do point out that only when beseeching the angels whose task it is to bring these prayers to Hashem (like by Machnisei Rachamim) is it OK.
It is not OK to simply lift your eyes to the heavens and pray to an angel, or even ask "the angels" to bring your Tefilos to Hashem, as it may not be their task to do so.
The prevalent Minhag is to say these Tefilos and to visit the graves of Tzadikim
(see Gemara Sotah 34b regarding Kaleiv, and it is also well known that Rochel Imeinu was buried on the road to Bais Lechem so her children, Am Yisroel can pray at her graveside. There are many more proofs for this being Ok, as well as proofs for the other side, but this isn’t the place for this lengthy discussion now)
However, when davening at a Tzadik’s grave one must be extremely careful to only pray to Hashem in the zechus of the Tzadik, or as we mentioned above to ask the Tzadik to be a Meilitz Yosher for us and our families etc.
2) Another example of Tefilah that may be affected by the above Machlokes (dispute) is the Shalom Aleichem Malachei HaShareis" which many say Friday night before Kiddush.
Rav Shlomo Zalmen Auerbach maintains that for the last 3 stanzas (i.e. BoAchem L’Shalom, Barchuni L’Shalom and Tzeischem L’Shalom) we say "Malachei HaShalom" as opposed to "Malachei HaShareis"(like we say int he first stanza) to show that we are only asking them to do their task of bringing Shalom-peace into our homes, in their capacity as Malachei HaShalom, and not praying to them in their capacity as "Malachei HaShareis".
Some have the minhag not to say "Shalom Aleichem" at all on Friday night.
In The siddur Avodas Yisroel (disciple of the Gaon of Vilna) it states that one needs to be extremely careful when saying "Shalom Aleichem...Malachei Elyon MiMelech Malachei HaMelochim..." not to pause between the words "Elyon" and "MiMelech" as to ensure that it is clear that the Malachei Elyon are emissaries from Hashem, and not a higher power on their own.